GM LS series V8s are some of the best engines around. Light, reliable with lots of torque and power.
There are Miata conversions. I have seen a few. On the race-track a 300hp turbo car was faster then a Ford V8 Miata. For racing with that much torque in Miata chassis a number of things need to be improved:
1. Chassis needs to cope with that much power and re-enforced.
2. Same for rear suspension and pick-up points.
3. Brakes. I just do not see stock brakes being sufficient for something that can go 200mph.
4. Aerodynamics, see above
All of the above will add more $$ to a car.
A Z06 is a great platform with all of these bugs worked out. If one can live with Miata-style creature comforts, then the final weight would be very similar i.e. strip it. Also, the price is too.
I have seen a Z06 with $10k of suspension mods, do 1:23 around Mosport with a good amateur driver (at a Ferari event!). That is TransAm car territory. I have not seen any Miata or Solstice or too many cars come close. By the way, it had full interior.
The cooling issues can be solved with proper components and correct air ducting. I never had any problems with 900hp car in a 1 hour enduro, AFTER I fixed the above. Oil at 210 and water at 180 to 190.
If one desires a boulevard hot rod, then the game is different.
For the wow factor, why not a V8 in a Lotus (Elise or Exige). Nobody has one yet! I have the front and rear suspension worked out, together with some aero work
There is the GTM, the SL-R and a few other kit cars. A steel space frame, 450 lbs engine, 100 lbs tranny, 400 lbs drive-train makes for a 2200 to 2500 lbs car.
Or a LeMans car for the street: