I recently swapped to the Michelin PS4 (staggered still) and all the tramlining is gone. Much better for a road car IMO. Would probably go that route on tires.
IIRC you'll need to do extended studs on the front to run the square setup and the spacer, so be sure to price that into the square...
2005 is a bit heavy for a track car and Limerock is a relatively short track. It'll be magical on the straights but doesn't handle super well relative to the GT350. Its a sweet car for sure, but its not something you'd want to get on the track a ton TBH (especially given the $500K cost).