You could try putting your figure in a cardboard box with either a small bowl of bicarb soda or sticks of chalk - just regular chalk you draw with, make sure the box has a lid and close it. The bicarb or chalk will absorb the moisture in the air rather than go into the figurines.
I tried the low heat source trick on a camera topper (most suggest a low wattage light bulb; I actually had it sitting on a closed laptop that I wasn't using). Not only has it dried out completely, it hasn't developed gooey spots, even though we're still in the rainy season that just won't end.
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