I ended up reading a lot more here and the forums for CR-V and Civic owners than I really wanted to, BUT I really wanted to know what part numbers were compatible, considering the problem of 6-speaker vs 7-speaker, etc. I ultimately found that both of the part numbers below for the 6-speaker configuration should work. If you have an LX or EX, don't get the 7-speaker head unit because you'll need an amplifier. You can tell the difference by looking: the 7-speaker has an extra port on the back.
As far as I can tell, as long as you match the number of speakers and the model number is NR-244UH, you should be able to perform this upgrade. There are similar part numbers to watch out for. NR-245UH is the navigation version, and you should NOT buy it. There are other versions of the NR-244UH, such as NR-244GH and NR-244KH, but I can't confirm those are compatible.
Why am I being so specific? Because I couldn't find the American part for a price I was willing to pay, but the Canadian part (which as far as I can tell is identical, and I've seen Canadians confirming their CR-Vs were compatible with the upgrade) was half the price. So now I have that on order, and obviously I'll update this thread again when I've had a chance to test the Canadian CR-V radio with a US HR-V.
6-speaker:
39100-T1W-A01-M1 (EX from US)
39100-T1W-C01-M1 (SE from CAN)
7-speaker:
39100-T1W-A41-M1
39100-T1W-A41CN
39100-T1W-A41CP
39100-T1W-A41RM
39100-T1W-A410-M1 (may or may not be compatible)
Navigation (INCOMPATIBLE):
39100-T1W-A62-M1
39100-T1W-C620-M1