Give the Sweep Kitty Rugs a try. TQ usually has them in stock. You might read through the last few pages of the sweep thread, I think they've got some new stuff out now that's supposed to be good.
Or Sorex, 24 or 28. They're pricey, but it's the best tire there is. I'd run the hardest compound you can get away with. With no sauce, you might try warmers. Also, see if you're allowed to use simple green to clean the tires. I've found I can soften them a bit.