So, it's wood. I wonder if something is eating the finish. Try wiping it down with the strongest alcohol you have.
Freezing may do something, but it would probably only slow it down, not kill it. Freezing works well for wood worm, if you're willing to leave it in there for a while, but I don't think it kills mold that well.
I wonder if drying it really well with a hair drier or heat gun would help? Just stop before it starts to crack.
You can't microwave it with the flange, and that's very risky with wood anyway. If there's moisture in it, you make either cook it or it could explode.
I'd think about the finish first and try the alcohol, or a very mild bleach solution.