I haven't tried it myself, but read recently that if you go over permanent marker with dry erase marker, then rub it off with the dry erase brush both marks will be removed. Good luck.
In a hidden place take the sharpie and make a mark, let it dry then write over the mark again and quickly wipe both marks. The new ink should remove the old. You may have to do this more than once. If it satisfies you here, go to the real mark you need to remove and repeat without letting the ink dry. Also try nail polish remover, again in a hidden place always when experimenting.
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