Since no one seems to have mentioned this, I'll chip in: one of the classic ways of cutting thin stock (veneer, etc.) without cracking is to lay it on a sacrificial piece of thicker stock (I would use Masonite, in this case). When you saw through both materials, the backing gives you an effectively zero clearance blade insert, and also helps to dampen any minor blade vibration. In extreme cases, double-stick tape can be used to hold the two pieces together.
I have made dark slides from the 1/16 black Garolite, but I was using a milling machine, the garage-shop equivalent of which would be a router. It shouldn't be surprising that this works very well, considering the millions of square feet of Formica countertop that have been trimmed to exact size using either an ordinary router or the specialized laminate-trimmer version.
FWIW, vertical-surface Formica is thinner than the usual countertop material, and would probably make a decent darkslide....