First, I agree that you need to check the rules of your organization to see if prep is or is not allowed. If it is not allowed, I would suggest cleaning them off well, saran wrapping them, deflating them, and keeping them in a climate controlled area. Beyond that, I don’t know if there is much you can do besides not running too much air pressure on the track and getting the kart handling well (A kart with a bad push will burn the fronts off in no time…don’t ask me how I know). I have found with Bridgestones, it is not the amount of wear, but the number of heat cycles that causes drops in time.
If prep is allowed, there are a whole world of options. I will not pretend to know what does work and doesn’t work, but there are options to soften up older tires. Check your local dirt track kart shop and see what they recommend.
You guys should go to a dirt track some Saturday night and see what goes on there. WD40 is not unheard of and is pretty tame compared to some things I have seen those guys put on their tires…