interesting idea Bob, but Solo is about being quick. However, you have a point, that if's all about fun and 'hooning' a bit without worrying about getting tickert than maybe slippery tires could be fun. More importantly, a built in handicap like this would force one to learn car control quicker, I should think.
But if it proves to be fun, and I become obsessed with lap times, I think the real answer is track specific tires, and one in a smaller than stock size both to lower gear ratio (low speed racing) not be trashing driver set & save weight where it counts. A set of lightweight rims and some Bridgestone streetable track tires would run about $800 on tire rack. Maybe not the ultimate wheels (Moma brand) but don't have to worry about bending a wheel in a parking lot. Substantial weight savings and 2" smaller diameter for 16" vs stock 18" (23" vs 25" overall)