Good to hear you figured out what was going on. Tires can be a big deceiver. They can look good with lots of tread, but when they get older, or have been parked for a while, they may not be much good.
My pickup had a bent rim and I didn't know it until I had to put on a new tire. Truck didn't shake or shimmy, but you could see the tire moving ever so slightly in and out while on the tire machine.
Another rim solved that problem.
