There is an easier way.
When you open a ticket the normal way it saves you data immidiately after pressing X.
If you use the "open all tickets" function (square button) you data will not be saved before you have opened all tickets and exit the trailer.
Simply open the ticket/tickets with this function and see if you get your desired car.
If not, quit to XMB without leaving the car trailer, restart the game, and repeat the process.
Quicker and easier this way.