Look at the RC car racing clubs. My brother used a light spray of wd-40 to break down the rubber and make the wheels stickier. Rubber renew used to refresh the rubber pullies in tape drives and turntables increases the flexibility of the rubber. Acetone may also work. Preheating (80-90 degrees) the rubber tires prior to an event also softens the material increasing grip. However, if you really want good solutions, you can buy the specialty tires they sell for R/C Formula 1 cars, or even mixing your own compounds.
I have also seen people post about using tacky glues. Check the rules of the event organizer as they may have limitations on what you can use to increase grip (it may make the arena unusuable)
There are a set of smooth-on products that are castable silicones in sub-Shore-A hardnesses. They end up being very sticky due to lack of skin but shouldn’t leave any residue. Ecoflex comes in 5A down to 000-35 (as in, pretty much gell water). Probably something around 00-20 will be good though I don’t have experience yet working with them to know which will give the best results; possibly 000-35 will… i should test that…
To apply, I suggest adding a thickening agent (THI-VEX) to make the gell brush-on with less chance of it slumping off while it’s setting.
You also may have an issue getting it to adhere to the current belt - worst case you can glue it in place with a thin layer of E6000 but definitely test. Also platinum cure silicones will be inhibited by latex and lots of other things - test and be prepared to clean off the tread if that’s the case. You can always make a mold out of something else then cast a ring onto that and glue it into place once it’s set.
Maybe some sugru? That stuff stays pretty tacky after it solidifies. Granted you wouldn’t be able to paint it on, but maybe if you attached little dots of it along the tracks.
Otherwise maybe it would be easier to just find softer rubber tracks.
There is stuff from Michael’s to put on the back of carpets to improve grip. Forget what it’s called though.
I just had a look at their online store, www.michaels.com, but did not see a listing to match my alleged memory. Worth calling the Broadway store. It’s been a while but I think they had that in stock at one point.