It looks like theres to much loose stuff for the crime fighters. The komodo dragon 2s work great on a wide variety of surfaces and they last longer then the crime fighters. The mediums should be fine in loose dirt but the harder it gets packed the softer you want the tire to be for more grip (in deep loose dirt the compound doesn't matter all that much so harder will just give you more life time). Its looks like everything but the jumps is packed about as hard as my local track and the komodo 2s work great.

After I bought my losi 8ight I tried out the stock losi step pins that came with it. Man those things give you loads of grip even in their hardest compound (silver) The step pins should dig into loose dirt/sand pretty well and maybe even better then the KD2s. They also seem to be lasting a pretty long time for tread life. If you can get them in your area I would try them out.

Softer foams will always give you more grip because it allows more tire to contact the ground. Of course to much grip will result in traction rolling so its trial and error. Also a hard foam might make the center of your tread wear out very fast. The panther and advantage racing foams have a very rounded profile which I don't like. The ofna molded foams are the ones I like most. The stock panther foams are good as well so just give them a try.