Need to unlock iphone for use with a different carrier.

I have an iphone 6, currently with AT&T. However, I want to use it on Verizon's network.

Here's the problem: AT&T states that my phone info/account looks spotty and they want me to see if I can get a copy of the receipt from Sam's Club (where I purchased it in 2014). The phone has been completely paid off, I've been out of contract for years, and my bill is current. AT&T states that due to the spotty records, they keep denying my requests to unlock it. I was advised by an AT&T rep that the spotty records are due to the way Sam's Club activated it? Something to do with it being on my account the whole time, but not actually on AT&T's network... which I don't really understand, but whatever.

So, how do I get this phone unlocked if I can't get help from Sam's Club, AT&T keeps denying my requests, Verizon can't do it, and evidently Apple doesn't unlock phones??? I'm really upset, because this is my phone. I paid for it in full, and I should be able to switch carriers with it if I choose to.