I use magic eraser with rubbing alcohol (91%) but be advised, you're not really removing those ball swirls; you are merely cleaning them out. The only way you can truely remove them is to sand and then you risk taking paint off to the point you may be forced to restore entire field. So long as you clean them out as best you can, regularly clean and wax the playfield, you should be fine.

You probably are going to have some brush marks but if you do the lines etc. with a script liner brush and thin paint it should come out decent.