I have a cub covered w 21st century fabric, its 28 year old and 4 years ago it was looking pretty ratty. the paint had oxidized and just looked dirty, looks like you have some mold in there to (just a guess). anyway I tried several different reducers under the hori stab and finally settled on monokote trim solvent (MTS). MTS dissolves the paint so if you spend to much time in one area you will expose the fabric or glue your rag to the covering.
I would wet viva paper towels and just wipe the surface. some times I had to make a few passes to get it clean. the key is to only liquify the outer layer and remove it. the MTS acts fast and evaporates quick, so it took little time to clean her up. maybe and hr.
Joe