If it is the tires, I am going to go with a set of new Coker steel belted radials that are narrower and larger diameter and have a bias-ply look to them ( The T5 has a pretty low first gear with my 3.75 rear end).
I strongly recommend against Coker tires from personal experience and that of others. I had a belt separate inside a tire in under 10,000 miles. Cokers have a pretty low reputation in the collector car community for being difficult or impossible to balance properly.
Corky Coker told the president of our club that if the car is being driven like a normal vehicle instead of just for show, he should purchase a set of Diamondback tires.
I have 3 sets of them and they're the best radial tires I've ever had on my Cadillacs and Packard. They're radials and have a bias ply look. The ones on the black car are the new Auburn radials and have a pie crust edge that looks even closer to the old bias plies. The close up is a Yokohama truck R700 truck tire with the whitewall vulcanized to it.
I think swapping your wheels front to back and back to front might give you a clue about the source of the vibration.
www.dbtires.com