I would suggest that the first thing you need to do is get proof that the debt is legitimate from the collection agency. They must be able to show that you actually owed T-Mobile the money they're after, or else they can't collect it from you.
Do not go through T-Mobile for this (as you already found out), they won't help, it's not in their interest to. Write a letter to the creditor. Be careful how you word this letter, though, as it may be possible to damage your statute of limitations defense by corresponding incorrectly. Something like this:
Dear sir or madam,
I do not have record of any debt to T-Mobile at the present. Per the FDCPA, I am writing to officially request you provide documentation of the debt, and cease debt collection activities until such time as you provide such documentation. Further, my understanding as of the last correspondence with T-Mobile was that my account was closed and current at the time; as such, I would request that you specifically include any agreement that I may have made that obligates me to pay this debt.
If you intend to pay the debt if it's legitimate (and I will say that given the facts you've presented and the dollar amount, it sure looks like a Early Termination Fee of a contract to me, so you may well owe it), you might include that at the end of the letter - that you fully intend to pay the debt if it is proven legitimate to your satisfaction, but that you do not believe it is. Be careful with that wording, though, because you may reset the statute of limitations if you promise to pay it unilaterally.
If/when they are unable to prove you owe the debt, I would send mail to TransUnion and ask them to remove it from your credit report.
Now, you're correct that the debt will fall off your report sooner if you don't pay it than if you do. That's an unfortunate result of our system; in order to have some consumer protection, they added the 'seven years' rule, but that does hurt people who pay old debts.
Do be careful though; if they file suit to collect, between now and January, your credit report may be more dinged than it is now. One bill that goes to collections is bad for your credit for sure, but it's a lot worse to have a lawsuit, especially if they win - and if this is truly an ETF you just didn't pay, they will probably win if they have their ducks in a row. Many collection firms don't, and they may well never file suit against you, but it may not be worth finding out.