You don't need comp school for TT, you want to contact the TT director Joe Sullivan. You can find his email on the Midwest or Great Lakes sites on the contact us page under the Press Room tab. TT normally requires advancement to HPDE 4 before being granted a provisional TT license, the director can provide you more information. You will also need to class your car (unless you run in TTU).
time trial unlimited? what can one expect when having an unlimited car but not at the class of other unlimiteds? like will a million dollar unlimited be pissed to see a unlimited miata ahead of it?
Well, the million dollar unlimited car driving flat out knows that the unlimited Miata is ahead only because his tires are heat cycled out and the shock settings are way off. He also does not allow the TTE Miata to pass because its likely to burst into flames.
As a more serious answer, I finished in the middle of TTU with what should have been an under prepped TT3 car. There were TTC cars that ran a faster lap than I did, and I didn't notice any ire on my part or any of the other drivers that they got beat by a "lesser" car.