Based on the high humidity conditions you described, I believe that the stock you have is dry-rotted. It may feel hard and sound, but it is not. It has in effect been soaked with moisture for long periods of time, letting it rot, and then dried out during the dry winter months, letting it dry. Year after year! If you go into an attic with poor ventilation, you will see trusses and chords that have the same thing. They seem very hard on the surface, but have a suspect hollow sound when you tap them. There are no holes or pockets in the wood per se, but the structure of the wood has deteriorated so that it is ineffect like a super hard sponge.
If this is the condition of your stock, I'm not sure that will ever be able to salvage it. If you do refinish it, forget using any rub on oil finishes (tung oil, lin-speed, tru-oil etc.) I would follow the advice of others on this board to get the stock dried out, and then figure out how to harden it up. One sure way is to use a product that is designed to be applied to dry rotted wood, that soaks in and hardens the fibers. (Min-Wax wood hardener.) If you put a really thick coat of this stuff on the dried stock, then the stock will soak it up and when the product dries your stock will be hard and sound. Problem is, you would never be able to stain it, as the pores would be sealed up. So, you would be left with its "natural" color.
Another thing to try, would he to apply a water based gunstock stain to the dried wood, to impart color, and then after it is thoroughly dried out again, to use a spray-on, super thin, poly-urethane based clear finish. Apply several coats and and then very lightly sand it with 400 grit sandpaper. (Call Brownells, and they will probably have it in a spray can.) This will seal up your stock and stop it from absorbing moisture again.
Hope this helps.
Mannyrock