It also helps to wipe the plinth with antistatic spray. Also the sound.I have a constant problem with very fine cat hair floating around in the air and sticking to clothes. A couple of weeks ago when more than I thought was stuck on my shirt, every time I did anything with a record on my turntable, it immediately had a number of hairs float over to the surface, drawn there by static electricity.
I finally realized the source (me) and also noted there was an obvious potential between me walking up and handling the record which is what drew the hair to the record. My turntable and all associated hardware is grounded, except the platter. But it does have an electro-static path to ground.
Here's the trick. When you walk up to your turntable, put your hand on a ground point, either the turntable chassis, the edge of the turntable -- something -- and hold it there for a few seconds. That discharges YOU electrostatically and eliminates the potential between you and the disc. Then go ahead and remove or place the disc. Now, only when I forget to do this, do I have static problems.
When you use a zerostat, the record must NOT be on the platter and YOU should be grounded to the turntable. Otherwise placing the discharged disc on the platter will still produce static electricity. I never use a zerostat any more, but just make sure I'm grounded when handling the records to/from the platter.
I suppose it might help to use a fabric software or de-static spray on your carpeting around the turntable stand/rack would help, but I haven't tried that yet.
A carbon fiber brush will work well if you are grounded to the table when you use it. If there's an electrostatic charge between you holding the brush and the turntable, all bets are off.