What are your goals for the car? Are you sure you want to spend $15-18k on your Z to make it faster in a straight line when $3k for an oil cooler, FI cat-back, test pipes, Stillen Gen 3, and a tune will net you about 40hp, some torque, and an awesome exhaust note? Add in some AutoX time and you'll have way more fun for literally 1/5-1/6 the cost of a TT build...
If you're actually racing disregard what I just said, but adding TT to a Z solely for bragging rights is a waste now that there are C7 'Vettes and blown 5.0s running around everywhere.