Where does the rain go that gets down the mast. That seems to be the most likely way for moisture to get in a boat. Get rid of that water and you'll have a dry boat. Ditto for any deck leaks, which are a problem in themselves.
After ventilations, the smallest of heaters can keep humidity away. Do you have excess solar or wind power (a dump load) that you can put toward a small heater and a fan? (Or even better, a duhimidifier.)
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