To follow up, I got the radio working.
I emailed back and forth with Buy Two Way Radios and eventually sent it back for an RMA. I spoke with their engineer on the phone while they had it and he was able to connect to repeaters without issue, so they sent the radio back. I received it yesterday. I got it all setup and I still could not connect to the repeater I wanted.
I started to think to myself. I could connect to the repeater with my KG935G+ and it's only a 5watt handheld radio. So, the only thing I never tried before was turning the power output down on the KG1000G+. I changed it from high power to medium power (which is 20watts) and low and behold, it connected!
I spoke with another operator; he told me it sounded great, a full 5x5. So, every other configuration setting I had was correct, I feel better about that.
We did net check-ins a little later on and I mentioned my success and what I had changed, and another operator said he had experienced the same issue once before with a Motorola radio he owned.
Can anyone explain, why lowering the power output of my radio would have made a difference? I'm just curious.