Well, here's my idea:
2 set of tyres could be included with the registration fee, those tyres will be previosuly marked by marshall using something like this:
It'd be pretty difficult to cheat, since you purchease the tyres with the registration and they are just labelled from the inside with your license number just before you get them. No other tyres allowed in the racing box.
This way you don't even have to bring your tyres, less stuff to carry to the track.
It's the easiest way to monitor everything. If someone complains about some tyres you just have to check your "tyre-log" with the ID inside the tyre. To improve controll even further you could only purchase one set of tyres at time, when they'd be wasted you have to return them to the marshall who will take note in the "tyre-log" so it couln't be used anymore. This way every driver will only have one set of valid tyres at time, making verifications easier.
You'd do this more sofisticated using speciall ink or logo, difficult to duplicate. To improve control even further you could only purchase one set of tyres at time, when they'd be wasted you have to return them to the marshall who will take note in the "tyre-log" so it couln't be used anymore, and then you'll get your new marked set of tyres. This way every driver will only have one set of valid tyres at time, making verifications easier.
I hope this will be helpfull.