I was testing this swap idea out today and after 80 minutes on the phone with 4 different people, the answer isn't a good one. Basically, only the physical stores can handle anything AUP related so skip the chat and sales call. Call a store.
But to make a long story short, the only way to get a Verizon compatible phone if you signed up on AUP under AT&T or TMO, is to start a new contract with the correct model. The Apple store is absolutely willing to do this but it's not a good solution. They would close out your current AUP and you would no longer have to make payments on that phone. They would swap that phone out with a VZW compatible iPhone and start a new AUP contract for you and reset that 12-month upgrade window. No bueno.
If you do want to switch to Verizon from AT&T or TMO, it's probably better to wait until the new iPhones are out. Until then, I suggest you express your displeasure to Tim Cook (tcook@apple.com) for false advertising.
While there isn't much to be done about this now, I think it's important for them to hear from customers on this issue.
If someone else has had luck with a straight swap out, I'd love to know.
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