After multiple hours on the phone with Apple and AT&T and a SIM card swap, this was the solution that worked for me w/ the T-Mobile "Contract Free" iPhone 6
I spoke to an AT&T GoPhone representative who actually figured out what the issue was through trial and error while speaking to other customers with our exact issue (no data on iPhone 6 w/ AT&T GoPhone plans).
Start by calling 611 and quickly get to a representative who can change your account's internet settings on the backend. At the time of posting here are the steps I followed:
-Call 611
-Wait until prompts are given, then press 0 for Operator
-During next prompts choose 6 for "More Options"
-Then at next prompts press 1 for "Technical Support"
-Then say "Data Services"
-Call will be routed to the correct queue
The AT&T Rep turned on a “feature” on my account by adding “NXTGENGPO” to my internet settings. This was all done on the backend at AT&T, not on my phone. Here were the steps I followed:
-Turned OFF Cellular Data (in Settings - Cellular)
-AT&T Rep added "NXTGENGPO" to my interned settings on the backend
-Turned Cellular Data back ON after it was added
-Cycled the phone off/on.
Lo and behold, LTE appeared on my phone after the reboot and data now works! When I asked what others should be asking for when calling, he said to do the following steps outlined above. I would assume this will work for an AT&T model iPhone 6, and for the Plus models, but of course, YMMV. Nothing else worked but this solution, including a complete restore through iTunes w/ carrier updates, AT&T APN downloads from unlockit, multiple "Reset Networks Settings" in Settings, a SIM swap, etc...
Good Luck!