Marc,
Another solution would be to 'mark' the hand out tyres for the racers to use. If they need a 2nd or 3rd set they can bring them to a steward in the sealed bag so we can open them up mark them up as well. Can be done by having a 2nd person when booking in on the day is done.
It's a sad state of affiars when cheating is being talked about in what is a competitive but fun meeting

.
Neil