Well if you aren't allowed to treat the track...there isn't much you can do. I would ask to see if you can at least clean the track, a leaf blower will work well to get rid a lot of the pebbles and dust, using a hose or pressure sprayer would be even better. After that use the softest rear tires you can get...whites are usually the softest. Unfortunately while they will provide better grip it may not be enough and they wear out fast.