I use Aquamix products, both acid and alkalis, as I've done some training with them. I've tried other stuff too, but so far theirs have been the most effective. The nano abrasive I use is a thick cream made by them and is called Nano-Scrub (unsurprisingly!). 500psi should be more than enough to rinse it out I reckon, it's usually just a case of rinsing off a few times and running the rotary over the floor again to get rid of the residues, but the spinner would do it in one pass and also give that extra cleaning power at the same time.
As for rinsing - kentucky mop, lots of clean water (and occasionally a ph neutral cleaner as well) and a wet pick up. I've never neutralised the floor chemically, as I've alway assumed the rinsing would have sorted that out, but I may start testing to see what kind of ph levels I'm leaving on the floor. Also, I've not used air movers as yet, but I'm going too now I've read up on them through this forum. As it gets colder drying times on hard floors seem to stretch out forever....

I might look into that IICRC course, it sounds interesting. There's so much to learn about stone, but not many good resources to pick up info from.