OK, here's my experience with an unlocked Verizon S7 Edge SM-G935V purchased from eBay and then used on AT&T's network, now that I finally got things sorted out.
My old phone used a different sized SIM card, so I couldn't just swap it into the S7 Edge. I went to the AT&T store, and they set me up with a new nano SIM card in five minutes, no charge. The AT&T rep also entered my new phone's IMEI number into their system. He didn't seem to care that it was a Verizon-branded phone.
After that I went into the phone's mobile network settings, and added a new APN entry for AT&T using all the info from the first post of this thread. After that, everything mostly worked, but it wasn't great. The Verizon firmware on the phone complained about finding a non-Verizon SIM every time I rebooted. MMS messaging didn't work correctly. I *think* 4G LTE data worked, but I'm not certain since I live in a spot with no LTE service anyway. I didn't try wifi calling or VoLTE (HD voice).
Next I used Odin to install the stock AT&T Marshmallow firmware onto the phone, G935AUCS4APK1. This fixed the non-Verizon SIM warning, and it picked up the correct APN settings automatically. I also verified that MMS and 4G LTE worked. Some previous posters apparently needed to give AT&T a different IMEI number from an AT&T-branded device before 4G LTE would work, but I didn't have that problem, and never contacted AT&T about any IMEI number issues. Unfortunately wifi calling did not work. When I tried to turn it on, the phone would think for a minute, then tell me wifi calling couldn't be provisioned for my device, and I should call customer support if I thought this was an error. I don't know if VoLTE worked but I assume not - is there any way to really tell, other than by subjective audio quality of the call? Also OTA updates appeared not to work, since there is an AT&T Nougat update available now that should have applied to the AT&T Marshmallow, but when I manually checked for updates it said I was already up to date. And lastly the AT&T firmware had a startling amount of junk in it, including an AT&T Address Book feature that kept popping up errors and that I couldn't figure out how to disable. So overall, this wasn't a great solution.
I used Odin once again to install the unbranded S7 Edge firmware for the 935U, G935UUEU4API3. Immediately I received an OTA update to firmware version PL4, so I could see the OTA mechanism worked. MMS and 4G LTE still worked. Wifi calling no longer even appeared as an option in the settings menus. Again, I assume VoLTE didn't work but can't confirm that for certain. Overall the U firmware gave me the exact same functionality as the AT&T firmware, except with a lot less bloat and junk, so I decided to keep it.
It would be great if I could find a way to make wifi calling and VoLTE work, but it appears AT&T just flat-out won't support these features on any non-AT&T-branded device. So if you're doing a Bring Your Own Device to AT&T's network, watch out. Here's a thread from AT&T Community Forums about this:
https://forums.att.com/t5/Device-Features/VoLTE-and-HD-Voice-Unlocked-Phones/td-p/4776203
I'm glad I finally get everything mostly working, but I'm peeved that it was so much hassle and still isn't 100% there. If you're buying a used phone and plan to use it with AT&T, I would definitely recommend that you spend the extra $20 to get an AT&T branded phone, instead of an unlocked Verizon phone or other unlocked phone that will only sort-of-mostly work. I wish I had.