Many "floatation" foams will become saturated with water, even though they are susposed to be closed cell...if so there is significant weight added to the boat.
Unfortunately very few, if any boats are properly built with sealing holes in cored structures. The builders take short cuts, Doing this properly takes time and makes a competative priced boat cost more. Unfortunate, but true.
As for removal of moisture in the core--very difficult to do with any usual drying techniques. I was down at the shipyard recently and one of the crews I often use, finally purchased a Hot Vac system. There was a Kadey Krogen 40 which is cored with a "closed cell foam"--and they had been drying with tenting, heaters and dehumidifiers for 6 months, after a peel of the outer layers of the glass. The Hot Vac brings the moisture out fairly quickly--if you have an extra $25,000 laying around.... This also takes time and costs because of the sealant used.
As for moisture meters--they are good tools if properly used. They are best used in solid cored boats, and after the boat has dryed for some time. Bottom paints and metals will give false readings. The cheapest type--capaticance, are fairly in-expensive--but I would borrow a good one, rather than buy a cheap one designed for lumber. If you have an interest, then read David Pascoe's article:
http://www.yachtsurvey.com/moisture_meters.htm
David is a bit controversial, but I find a lot of truth in his writings.
The best "solution" for a cored structure, is to replace the core which is wet--especially in our sized boats with limited core damage. Larger boats, need peel, hot vac and drying, then relamination. Neither is cheap or easy. That is why I advocate properly sealing before there is a problem.