Yeah, being within that distance of a broadcaster is the real problem at hand. Based on your symptoms, I'm assuming there's UHF TV broadcast on that tower in the 500 MHz band (which is almost all that's left of UHF TV). TV typically runs tens to hundreds of kilowatts, and any internal or external mixing products of TV broadcast may resemble noise due to the DTV modulation. FM is more easily controlled and the harmonics aren't in-band (fourth harmonic ends at 432.2 MHz), but that still requires strong filtering. To do an actual check of your RF environment and noise floor, you'd need a good spectrum analyzer that stays linear up to at least 10dBm; most quality equipment is rated up to +30dBm.
If you've got noise that appears to be in-band but cavity filters improve the situation, you've probably got intermod going on. Band-reject filters near the antenna can help with that. If filtering near the receiver doesn't improve in-band performance to a satisfactory level, PIM may be at play. Right now, intermod and overload effects could mask a generally crap noise floor from unintentional radiators; don't expect to dive in with hundreds of dollars of equipment and hit thermal noise floor (though you'll have to spend a little bit more to avoid PIM and ensure linearity of any active components). A noise power of -125dBm/16 kHz is pretty typical for a quiet area, compared to thermal noise floor at -131dBm/16 kHz. HDMI/DVI are particularly egregious noisemakers on UHF LMR bands, especially with AliExpress-quality cables. LMR-400 would make a mess of your RF environment.
Overload effects don't cause CCRs to not be heard, it simply knocks out their ability to hear. Any RDA1846 design will show desense on almost any rooftop antenna anyways; they're meant to be used with unity-gain antennas attached to the unit and work rather well in that scenario. Desense on the stock antenna or equivalent is only encountered in rather exceptional RF environments.