I went to the liquor store on Monday night, and bought two big bottles of their cheapest Vodka.
Don't worry - I didn't drink any.
The problem I have is terpene, which is a strong chemical that occurs naturally in many plants, and is what gives wood that "woody" smell. It's also the basic ingredient of turpentine, and is the main reason that even natural, unfinished woods are not as safe for the chemically sensitive as one might expect.
Ethyl alcohol is a very powerful, natural solvent, and vodka is a fairly economical solution of pure alcohol and water. Rubbing alcohol is not pure alcohol, but has acetone and methyl isobutyl ketone added to make it undrinkable, so it is unusable for our situation.
Anyway, I soaked some rags with vodka and set them on the sauna bench, which had been moved to the living room. The alcohol dissolved the terpenes and then evaporated. By morning, the whole house smelled like a sawmill. And once the rags were removed and the bench had dried, the wood smell was nearly gone. Success!
I'll probably have to rub vodka on the rest of the exposed wood inside the sauna several times to get the same results, but I'm very encouraged by the results so far.
And I don't have to wait until the sun comes out this summer. That starts sometime in April here in Texas.