Now if the mold is all over, bad enough, fuzzy, able to be felt over just a few stains. I myself would have it re-felted to solve the issue, as no cleaning will cure such a bad case.

If just light, dusty mold, just a corner… the only thing I can think of is bleach and water. Maybe make it a very diluted mix and instead of wiping it… mist it from a spray bottle so its barely damp. Then let it dry. Then repeat a few hours later. Do this slowly till the mold finally dies while not bleaching the felt.

Or call up pool halls or even pool table sellers and see if there is a chemical or product on the market. Being a slate base, I am sure they have had this issue before.