Hello! is anyone still here?
Furnace-heated air is usually very dry, and when the RH difference is great (as often happens in winter) just about any wooden humidor will give up moisture right through the pores in the wood. Unless you want to apply a couple coats of polyurethane to your humidor -- or switch to a coolerdor or ammodor -- there's not much you can do about that.
But I have a couple of suggestions.
First, bear in mind that wood shrinks a bit as it dries out, and that includes the lip of your humidor; even if it seals beautifully most of the year, it could develop a "seasonal" leak during winter. An easy fix is to cover the lip all the way around with a single layer of blue painter's tape -- better looking than ordinary masking tape, and the adhesive isn't so aggressive that it pulls splinters if/when you remove the tape. Use an X-Acto knife or razor blade to carefully cut the tape at the corners, so it makes a seamless a seal as possible.
You can always transfer your cigars to ziplock bags and then store the bags in your humidor; that will keep the cigars from drying it, but doesn't help keep the humidor itself properly humidified. While your technique of using a moist (but not too moist!) sponge probably won't do any damage, be careful not to apply so much water that you ever see any water standing on the surface; this will cause the wood to swell, possibly making any leaks worse or introducing new ones at the joints in the wood.
(If you decide to move the cigars into another container, I suggest leaving a wet sponge resting in a saucer or other container in the humidor to keep it from getting too dry over the winter months. Obviously, you can't do this while the cigars are in there.)
I'll echo sy7vester's recommendation to use Heartfelt beads (
www.heartfeltindustries.com). While the air in my home probably isn't as dry as it is in yours (the hygrometer at my desk is showing 35%), I was having a problem maintaining high-enough humidity year-round using the usual green-foam and gel-jar humidifiers. I switched recently to Heartfelt 65% beads, and my desktop humidors now stay at 65% (my RH preference), give or take a point ... which could be hygrometer error, even with a calibrated digital hygro. And my humidors recover quickly after I open them to add or remove sticks. I'm not connected with Heartfelt, and I'm still a new customer, but I gotta tell you they work well.
FWIW, I bought a half-pound of bulk beads, washed out my gel-jars and put the beads into the jars, then returned the jars to my humidors. Think of it as recycling, or just being cheap.
You could also use Boveda packs (the recommendation is one for each 50 sticks capacity, plus one additional for the humidor itself), and they work well too; but even though they can be recharged, eventually they have to be replaced. I expect the beads to outlive me.