WRUH396

This is the kind of stuff we see.  This one is actually on HF but we have seen this noise much higher into VHF/UHF as well but this type of unnatural spikes across the band or covering multiple channel slots is what you want to find.  Look at the visible jagged spikes below.   

The other thing to keep in mind, though not as likely as you mentioned you tried a few different radios, but as 935 was pointing out on my post that a lot of this SOC/SDR style, cheap Chinese radios have the front-ends as wide as a barn door and are susceptible to desensing, mixing and intermod.  There is an area near where I live by the airport and county dispatch that any Baufeng, BTECH or other cheap SDR gets slammed and sometimes it is so clear it sounds like they are dispatching right on GMRS or our UHF frequency but we don't get that at all on Yaesu, Kenwood or Icoms. 

People are covering some a lot of good info above.  As one that spends a lot of time on VHF/UFH I can tell you there are some really pesky interference sources lately.  The extra wide or drifting carrier is kind of a telltale sign it is not likely a radio.  The most common we have tracked down recently are: 

Switching Power Supplies 
Cell and USB chargers Home and Auto (They switching powers supplies) - this is very common in cars and comes and goes as the device charges
Solar Chargers and Grid-Tie Inverters - people are adding more and more solar arrays by the day. (Worse during daylight hours) 
LED lighting systems

If it really gets annoying buy or borrow a cheap SDR donglem go mobile and use that with a portable laptop to track it down.  Also check your own house as well.  I will see if I can find a spectrum pic of some of the madness we have seen.   

SUPER long-time CBer. VERY long -time ham and yes, now repeater owning GMRSer.
Besides just trying to be as cool as Randy, I wanted a way to be able to talk to my family without the internet or being at the mercy of some technocrat app like Facebook.  After all, The Zuck shut even my messenger down that I use with my children that drive to school nearly 30 miles from home.  Plus we live rural and cell coverage is just getting up to speed out here anyway.  Only one of my sons got his hammy-ham license and my wife and daughter have no interest at all.  They (The Facebook Police) would even look at or use AI to look at our private texts and shut My messenger down during elections, inauguration, J6, again as we (The US) began to support the proxy war in Ukraine and any time I mentioned the global warming coincidence AKA 'Died Suddenly'.  Now, most the time they would reinstate me after a week or so but this time they permanently suspended my account.  Long story short I needed or wanted a backup way I could communicate with non ham licensed family members that can't easily be shut down during your average TEOTWAWKI--SHTF event so now we use the encrypted Signal App and our family's GMRS repeater as a back up.

Well of course when I am doing serious testing or just want to let down what's left of my hair, it's GMRS and also of course most my friends are experienced licensed ham radio operators and yes, we do indeed talk 'Radio' and about everything including ham radio and ham frequencies.  IMO the best range tests should include and ongoing conversation to identify holes or lack of coverage.  And yes, I am sure some of the jargon bleeds into our GMRS conversations but those are the guys that will recognize problems with the signal or give me the best reports and ideas on how to make improvements.  The only real difference though that I think might stick out to GMRSers is our group tends to me a bit more anal about IDing to stay in compliance than most the other GMRS only users I know, not that we care though, it's just what we are used to.

Like other hams, I don't feel I must give anyone an explanation per se but if this helps pure GMRS guys understand when and why I personally use GMRS then I will share.  

Now to find that Affiliate Link for the Mossberg Parts mat... 

I'll have to dig for final pictures but here was the pictures from our "trial" unit. Pretty much all is the same other than we replaced the connectors on the ICOM with BNC (it was an orderable part from them) vs the adapter we used on this unit. For this one that was VHF that basically the only change we made. The UHF has a similar duplexer but in silver. That really the only way to know them apart without turning on the radios. I'd have to dig for the parts list as this was done back in 2013. 

 

We have 2 repeaters for our SAR group based on portables. Both use modified ICOM handhelds (Swapped MX antenna jack for BNC Jack from ham radio. I used a very small duplexer made for 15 watts or less. They are controlled with a vox style controller that plug into the mic jacks. Battery eliminators on all radios with a 3AH Gel Cell mounted in the pelican case. VHF is 2.3 watts out to the antenna on high power. UHF is 3 watts out to the antenna. They work as intended but if they sold the RT97 at the time I would have ordered it. 
Both are in a small pelican case. That was part of our use case. We have a portable mast with 25' of LMR400 and Unity Gain antenna for each. 2 guys can walk up a trail with the case, antenna and cable and set it up on a hill to give us that extra range. It doesn't get used all the time, but the location it was built for works well. We are primarily VHF so the power is not perfect but is better than hauling our big repeater up to a site with a 6 wheeler. The UHF has only been used for training. Works good, but as said if I had the RT or Midland option at that point I would have gotten those. 
In the end we have about $1000 per Pelican Case. The radios were purchased on state contract for $299 each, Duplexer was $100, repeater controller was 100 and another $200 in battery, RF jumpers, bulkhead mount and charger for battery. We went with the ICOM LMR radio because we use public safety band, and to be honest they are way better than any CCR you will try. The receiver on the ICOM is very hot and is very narrow to the band in use.

SUPER long-time CBer. VERY long -time ham and yes, now repeater owning GMRSer.
Besides just trying to be as cool as Randy, I wanted a way to be able to talk to my family without the internet or being at the mercy of some technocrat app like Facebook.  After all, The Zuck shut even my messenger down that I use with my children that drive to school nearly 30 miles from home.  Plus we live rural and cell coverage is just getting up to speed out here anyway.  Only one of my sons got his hammy-ham license and my wife and daughter have no interest at all.  They (The Facebook Police) would even look at or use AI to look at our private texts and shut My messenger down during elections, inauguration, J6, again as we (The US) began to support the proxy war in Ukraine and any time I mentioned the global warming coincidence AKA 'Died Suddenly'.  Now, most the time they would reinstate me after a week or so but this time they permanently suspended my account.  Long story short I needed or wanted a backup way I could communicate with non ham licensed family members that can't easily be shut down during your average TEOTWAWKI--SHTF event so now we use the encrypted Signal App and our family's GMRS repeater as a back up.

Well of course when I am doing serious testing or just want to let down what's left of my hair, it's GMRS and also of course most my friends are experienced licensed ham radio operators and yes, we do indeed talk 'Radio' and about everything including ham radio and ham frequencies.  IMO the best range tests should include and ongoing conversation to identify holes or lack of coverage.  And yes, I am sure some of the jargon bleeds into our GMRS conversations but those are the guys that will recognize problems with the signal or give me the best reports and ideas on how to make improvements.  The only real difference though that I think might stick out to GMRSers is our group tends to me a bit more anal about IDing to stay in compliance than most the other GMRS only users I know, not that we care though, it's just what we are used to.

Like other hams, I don't feel I must give anyone an explanation per se but if this helps pure GMRS guys understand when and why I personally use GMRS then I will share.  

Now to find that Affiliate Link for the Mossberg Parts mat... 

Radioddity has a 3 day sale on its DB20-G for $85 down from $109.
It’s the Midland killer, easy to use out of the box, mini-mobile (fits in the palm of your hand), 18 watts, cigarette lighter plug and many many satisfied users here on this Forum. 
@KAF6045is the only user here that published power problems with his unit which was replaced  
Meets all of your requirements: ask questions if you have any. 

Unless things have changed, the MXT-115 (and likely the 275) are NFM (12.5kHz) only, and do not support "proper" GMRS 20kHz bandwidth.
OTOH: my MXT-115 was at least reasonable in power output (only about two watts below marketed 15W). In contrast, the DB20-G I replaced it with (to get 20kHz bandwidth, and extra memory slots to store repeater configurations [for repeaters I'll rarely be in reach of ☹️ ]). Two samples (returned first for replacement) both come in well below spec using the same measurement configuration. Others report reasonable power, but not mine. Sold as a 20W, manual documents 18W, mine puts out about the same as the MXT-115 on 462 Simplex, and even less than the MXT-115 on 467 repeater. "UNLOCKED" into a dummy load, it shows about 12W on 467, 13W on 462... But rises to 20W in the 2m band!
Decided the power level was close enough to the MXT-115 so kept the second sample -- 20kHz bandwidth and extra memories made a reasonable justification (in Locked GMRS mode, it provides only 9 "custom" memory slots, and the rest are receive only for out-of-band receive -- Unlocked makes all memory slots usable for GMRS [given an RT97 repeater alone has 16 memories for the 8 repeater channels, so one can set up two configs per channel, having more than 9 custom memories is desirable]; granted, they also become transmit capable on non-GMRS frequencies). Still need to cut the power plug off and rig a wiring harness with in-line fuse to wire to battery, and add a quick-disconnect at radio end -- the MXT-115 is double fused; lighter plug and in-line, and has a QD coupling near the radio.
 
 

The most popular Ham 2M repeater in my area (Utah County 146.76) has almost no tail to where slower radios like Baufeng UV5R may no indication or tail which seems to actually encourage "Kerchunking" since people do not know whether they have hit the machine or not. 

The family repeater I put together had a decent squelch tail but I know what you mean about not being able to tell when you have keyed it up.  I was not sure what kind of tail if any I would get from my RICK style repeater but it surprisingly has a decent tail on it.  If not that would have been one of my first priorities. 
My thought is you may see some hams that look down on courtesy tones since the it feels too CBish, yet in my mind they do serve a purpose beyond cycling the transmitter relays.  Without even thinking about it, it lets me know if the other operator unkeyed or otherwise dropped out of the machine versus the possibility that it is my receive that has changed, especially when mobile.  Certainly there are plenty of ham repeaters out there with courtesy tones and not once have I ever thought to myself, "oh this tone is so annoying".  I really have come to the conclusion that there are many people that just want to bellyache and complain.  While, I would not add some CB 5-tone "roger beep" I think a modest courtesy tone is a great addition.  Even NASA uses tones for the astronauts.  ?

I like that....   

If you can't find the Midland in stock, I  have found the Browning BR-182 spot on for the GMRS frequencies and frequently find them under 30 bucks.  It even works fairly well as a base antenna with the ground-plane kit, no it's not a 1486 or something but not too shabby for the money. 

I like courtesy tones for digital radio, where there is no obvious break, but not for analog. I prefer a slightly extended squelch tail on analog. 
Dealers choice, as the say.

Can any of those be remotely controlled using DTMF? Especially #2 - Transit Function?

The most popular Ham 2M repeater in my area (Utah County 146.76) has almost no tail to where slower radios like Baufeng UV5R may no indication or tail which seems to actually encourage "Kerchunking" since people do not know whether they have hit the machine or not. 

The family repeater I put together had a decent squelch tail but I know what you mean about not being able to tell when you have keyed it up.  I was not sure what kind of tail if any I would get from my RICK style repeater but it surprisingly has a decent tail on it.  If not that would have been one of my first priorities. 
My thought is you may see some hams that look down on courtesy tones since the it feels too CBish, yet in my mind they do serve a purpose beyond cycling the transmitter relays.  Without even thinking about it, it lets me know if the other operator unkeyed or otherwise dropped out of the machine versus the possibility that it is my receive that has changed, especially when mobile.  Certainly there are plenty of ham repeaters out there with courtesy tones and not once have I ever thought to myself, "oh this tone is so annoying".  I really have come to the conclusion that there are many people that just want to bellyache and complain.  While, I would not add some CB 5-tone "roger beep" I think a modest courtesy tone is a great addition.  Even NASA uses tones for the astronauts.  ?