If you are going to have a "gentleman's agreement" per tires, have a small trophy /pizza party just for the guys on the right tires. Dont allow the HOHOs to eat any pizza. Sounds trivial but racing among friends is the best.
Some guys just like to go fast and look good on the results page. Some guys, as they get older/wiser, like to race WTW. The actual speed is irrelevant. Slower cars give you time to flip each other off on the straights.

The actual tires; Falken gave me some tires @ 40$ per for the Crap can races way back. They were fine until they got overhot and then went greasy. They also dried out and were rocks at the next race. I dont use falken anymore. I pay for Dunlops, DZ101 and Stars, and will run the Rivals or RS3 . The RS3 are cheaper and seem to run almost as fast as the Rivals.

Spec the max width, dont let it get into a tech battle.
Maybe spec "all 4 shall be the same size".
If the intent is cost containment , contain it.

I am happy to see new racers posting here . Welcome.
Please voice your tire concerns , and maybe how you came to race with SCCA. So that we have some idea how to do it better.
Thanks, MM