Hey ricks6845. It's such a bummer to read about this awful mess you're in. I'm sure this has been a frustrating experience, and I'm sorry it's dragging on. The short answer to the title of your post is: you are doing exactly what you need to be doing! I'm glad to hear you were transferred to an escalation team - if the Solution Center folks are asking for IMEIs for your Trade-In equipment, that would lead me to believe that we need that information to research the issue and hopefully make this right. While we should never provide labels for the T-Mobile Return Center Texas for trade-in equipment, it's my understanding that trade-in devices may be shipped to Assurant by our warehouse team when the IMEI is associated with a trade-in. It sounds like this may be why the specialist you spoke with is asking for IMEIs.
If you were paying on a financing plan with AT&T, usually they'd have a record of those IMEIs on the statement where you'd be billed for any final balance - that's how we match them up for Carrier Freedom when we reimburse customers for switching costs. What about sales receipts from when you purchased the devices? Some of the die-hard Apple fans here might know better than me, but would it be possible to get the IMEIs from iTunes or iCloud by logging in with the AppleID that was associated with the phone? I know you can get your current device's information there, just wondering if they'd have historical information as well.
Since the Support Community is a user forum, moderators here don't have the ability to access accounts or perform this research ourselves. I do think you're in the right hands with the team you're working with, and will cross my fingers that you're able to find those IMEIs somehow!