[LanceGT4]

Could be right about the rear mounts. Get under the back end and look up at the mounts. One of mine had oil drips, the other was dry but still bad. On a 99 with about 90K miles on it. It did NOT like sweeping on ramps, at all.
How bad was this before you changed tires?
Check your tire pressures. mine seems to like 36 front and 42 rear. I hear that some run even higher with more that 6 higher to the rear. This is for highway cruising in the Pac NW.

Oh, re-read your post. SCCA racing you probably check air pressure first thing.
Let us know what you find