Sharkamino has provided an excellent cleaning guide. give full wet clean a try.
Check the gound to your preamp.
EDIT: Sorry I just noticed you said you tried your records on a friends player and its fine. Still doublecheck your ground, and do you have a spare RCA cable to change out between the SL and your pre-amp? Clean the contacts RCA on the back of the SL with whatever contact cleaner you have available (Deoxit, CRC. WD40)
The SL may need service, do you have a local shop, or are you good with electronics? You have kind of eliminated the records and the preamp from the sound of it
Thunderon Brush may work better than a carbon fiber brush. Or the Mapleshade has a ground cable. If you still get lots of static awhile after full soak wet cleaning causing hairs to stick to the record try a Zerostat or a plasma lighter.
https://www.amazon.com/Milty-5036694022153-Zerostat-Anti-Static-Blue/dp/B0033SHDSS Used this in the past, but if your weighing reagents into flasks you might still have an issue with any water there.
Leather cuts down static, so does cork
But it sounds like you have an outrageous problem with it, that mat material may not be able to solve
Having a wood fire going will drop your humidity, do you have a humidifier? If not I would get one....
EDIT: also Zerostat