My suggestion would be to cast the slicks in two pieces or halves, much like the styrene slicks included with the old AMT "Old Pro" Nova SS kit. I'm not sure how resin reacts to being heated up, though. If it gets pliable like styrene, you could warm up two cast slicks to soften them (one right, one left), flatten and widen the bottom, then add the wrinkles after it re-hardens. I don't think the softened resin could stand being stressed and stretched like a rubber tire can to create the sidewall wrinkles.
You could just add material to a two-piece slick to get the bottom wider, remove some to get the contact patch flat, and add or remove material to create accurate wrinkles. Lots of work for sure, but it sure would be cool.
I may just have to try it...