Not 100% sure on this but -
Is your AT&T 6 plus unlocked? If so, you can just walk into a Verizon store, get a sim and get the phone activated on a new plan. Once your established on Verizon, you should then be able to upgrade the line through the iPhone Upgrade Program.
I actually had to something similar, ironically going from Verizon to ATT. At the Apple Store I was unable to transfer carriers because Apple can only do upgrades on the same carrier. The only option was to buy the phone at full retail. Luckily there was an ATT carrier store near by. I setup a new plan, added my Verizon phone as bring your own device, popped in an ATT sim and I was good to go. I was then able to seamlessly upgrade my line at the Apple Store.