My car sits on skinnies and DRs all the time. I drive them on the street - all the way to SDR. I do not have any other wheels/tires at this moment (sold them), but my car is exactly what you are looking to have show up in every other aspect - full interior, daily driveable. I know that I would not make a Quick16, but like to run for fun.

Personally, I think you should have TnT for anything that shows - any tire, trailered, etc. No limits, just let them know that the track will not receive full prep. That should keep serious competition guys away.

For the Quick Street 8/16, I would suggest that you impose tire and suspension rules - stock suspension ( no backhalves, etc) and DOT tires with a UTQG rating at 140 or higher. Most racing organizations do that. That would eliminate most competition, DRs, R-compounds. Just a suggestion.