i’m not sure if the car u get from a ticket is generated from the moment you open the ticket, or rather from the moment you receive the ticket. i'd presume the latter tbh, in which case you'll find the same car even after a reset.
you could always make a backup of your save just before the race you know will get you a ticket and then restore and re-run it if you don't like the car.
hard-resetting the ps3 whilst receiving anything in gt5 i think would be very risky. the auto save only has to kick in for a micro-second and it could corrupt your data on a reset.
would be interesting though to know exactly when the random car is chosen, and if it's truly random etc.