Down here in the Ye Olde Skunkworks, it can get rather dusty. I do use a Shop Vac to clean up first (a small one with filters). I do this to make sure there are no larger objects like the occasional body screw, or in my case down here, a small moth/bug.
Then I use masking tape. Nothing has proven to work better than this method as it actually picks up the small particles, not just move them around.

It leaves no residue and is simply a very inexpensive and effective method. I run about 4 or 5 laps and change the tape, repeat. Done.
Then just racing the track. I do this before any product review road testing and before our major race events.
Both the MIDMO and Show-Me tracks used Satin. After the first coat has dried, I use a tack cloth to clean, then two more coats.
We race it all here. Rubber, Fish Foams, Standard foams, PG urethanes, Quick Slicks silicones. From 1/24 vintage thingies to stock 1/32 cars. What tiny amount of "rubber" silicone might pick up or clean isn't hurting a thing. The rubber that is worn in, stays in. This isn't necessarily improving the grip surface and removing loose portions of it isn't really a bad thing. It is more related to the smoothness your surface becomes over time by racing. The smoother it is, the more tire contact to the track. And in just a few laps with the stock or rubber tires and what small amount has been cleaned, just gets "baked" back in again.
Some clubs have all sorts of rules and restrictions for tires, tire cleaning/treatments, etc. These simply do not exist here. Anyone that has watched the race videos of our Showdown Series, or driven here will attest that there is no grip issue. Each year since the Show-Me rebuild, the lap times are just getting faster. The more action this track sees, the smoother it gets.
Again this was a good testing and appreciate the effort. I hope your track serves you and your racers well.