Until you use acetone, the next strongest cleaner are some Storm products like Proacta Clean which contains denatured ethyl alcohol. You can buy it straight from hardware stores and paint stores and places like Home Depot.
I have encountered old belt marks that nothing but acetone or cleaners that contain acetone, like Tenth Frame's UltraClean recommended by Brickguy above. (Jim, it does contain acetone, among other thigns, which is why it will remove anything.)
Now it's not a mortal sin to use acetone to clean off stubborn marks, but it should not remain in contact with the ball for any extended period of time, like 5 seconds is too long. ALL pro shops use acetone to remove excess insert glue. Best method is to place a tiny amount on a clean cloth and use the cloth to rub the bad spot.
Reminder: Acetone dissolves plastics (resin, urethane and polyester all belong to the family of plastics.) in large enough quantities, so be careful!!!!
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"Just because you can do something does not mean you should do it."