Repairing worn autocross tires

The Falken Azenis on my 91 Corvette have about 2 seasons of runs on them and are down to the wear bars.  At my last event I had a rear tire punctured by a screw.  The puncture is right in the center of the tread.  No reputable tire stores will fix the tire since it is down to the wear bars.  I think I can get a less than reputable repair shop to fix it.  I have new RE-71R's on order that are going on new Z06 style wheels, however I would like to get one more event on the old Falkens?  Would I be asking for disaster if I run on an old plugged tire?

In reply to BadPax :

I think the plug is the least of your worries on the tires. but I've plugged old RE71's and just called it good. 

NAPA sells the "brown string" plug material with and without the kit.  I've done a few myself.  It's not difficult, just follow the directions. 

Use the NAPA stuff though.  I've tried some other kits that were a waste of time and money.

Thanks for the input.  I am running in a very small class and have the lead fairly well in hand so I was hoping to save a few bucks and run the Azenis as long as I can.