I submitted my new 1020 that I payed in full a few days earlier and got denied on their portal - It said I reached a limit of unlocking, although it was the first time I've ever asked them to do so.
I contacted them via chat and referred them to the unlock case and the support rep was able to get the request through and approved since the phone wasn't subsidized and I've never asked them to unlock a phone before.
With that said, I have been a customer for over three years and no longer on a contract (month-to-month now), so they may have been more willing to cooperate and keep me happy, opposed to to someone who's never used them before. I didn't plan on leaving AT&T either, but wanted the ability to use other SIMs if needed.
The FCC guidelines state that all the guidelines don't fully go into effect/enforcement until Feb. 2015, so it may be possible that AT&T doesn't have to serve those who are not or haven't been customers. Their website's terms for devices unlocks specify that you need to be a current or former AT&T customer and your phone must be paid off.
If you can't get AT&T to cooperate, you may want to try T-Mobile themselves. Tell them you want to be their customer, but you have an AT&T phone you want to bring with you. I've heard of some cases where carriers will unlock others' phones so they can be used on their network. A last resort may be to use a well-reviewed third party. You'll have to pay, but the reputable ones tend to give good service (although I personally can't attest to them as I've never used them).
In general if you are getting a new phone I'd recommend getting it factory unlocked, if possible. You'll save yourself a headache down the road.