"Did anybody ever hear about that guy who used the industrial house drying unit to suck out the water? Did it work? I would like to avoid re-coring if the balsa isn't rotten."

Yes, this approach worked. The boat that was dried had wet core throughout the entire bottom (when test holes were drilled, water came out in some areas). Holes were drilled over the entire bottom and rotten areas of core were removed. We were able to take the boat from a virtually saturated state, to acceptably dry in about 3 weeks. The down side is that this equipment is extremely expensive to operate. Had the owner not been a friend of ours the cost of drying the boat would have exceeded its value. When the boat was dry, it was left with thousands of small holes into the core. The only way to fix this was to fill them all and vacuum bag a layer of thin fiberglass cloth over the entire bottom. This turned into a pretty major project and although it only took 6 weeks or so if you have the ability to keep your boat out of the water all winter, it could be done without the drying equipment.
It sounds like people are looking for a simple solution to dealing with core moisture. The reality is that all of the solutions are pretty huge projects, and its just that some of the people doing them are willing to take on jobs of this scale. If you can put your boat inside a heated shop for the winter and drill holes (1/8" or so) on a 1" pattern over the wet areas you will be able to remove the moisture, then you will have the task of filling all the holes and fairing the bottom. If you are looking to do it quickly the easiest way to deal with it is to map out the wet areas and remove them and replace the wet core. It;s been said before, but its worth repeating. The most important step is to definitively stop the ingress of water.

my $.02