anyone ever try cutting rubber? I was approached by a car dealership to cut rubber mats for truck beds due to no availability. I'm apprehensive, I think it would require a up cut bit, but also all the rubber residue around my table and in my dust system would be a concern(probably too hot for dust extraction) and just having that kind of contaminate in my shop.
Reciprocating knife would be what you would need, not something that can be equipped on your machine though. Video here, https://www.youtube.com/watch?v=dYFpgsoOyr8, 3:08 is when we cut rubber with it.
You could maybe get away with a burr bit to essentially grind the material away, but not sure how long the tool would last. And all the downsides you've mentioned regarding dust collection and overall level of mess.