I've been wondering if I wrapped the mast step in those high absorbant chamois, if I could head it off. They would have to be removed frequently, but I wouldn't mind if I had to swap them out weekly, or so.
However, I would say that a gallon or two collects after a storm. Not sure how much they hold. It would be silly to use a dozen of them.
No way I would trade a little water in the bilge for a wooden mast.