In my experience, quartz requires patience due to the hardness. It cuts slow and you will find yourself using more force than you need to resulting in popping the stone off of the dop. I can't tell you how many times I've done exactly that... even these days knowing better I still do.
When I do quartz, mostly amethyst these days, I use a REALLY old crystalite 3k aluminum lap. This thing is at least 30 years old and still prepolishes nicely. With quartz I almost get a polish on the facets. I've tried the newer versions of this lap, and they are complete trash, as they have an imperfect surface which causes deep scratches on the surface you are trying to prepolish. I'm going to have to get a new pre-polish lap soonish as I can tell that my trusty 3k is nearing the end of its life. 😔
For polish I use 60k diamond on a Batt.