Depending on how it was gutted That alone could be your problem with the backfireing. I would doubt that they have a factory tune for any T-bird with the cat gutted like an empty box (creating wierd exhaust flow)
I would make a real crossover pipe and remove the cat altogether or replace it with new and would be willing to bet the backfire would go away.
I just got my new Thunderbird yesterday and only on hard deacceration does it give any hint of a noise that could be confused with a backfire!(note I said could be confused not is a backfire)
It has factory installed big bore, short tors, the upgrade filter and programming I really cant see any reason to mess with the tune it has The bike is a pleasure to ride and always very responsive no matter what I'm doing.