I have some wet spots on my 33 Morgan's deck near the mast boot. The boot is completely sealed, but nonetheless there are wet spots. I talked with a fiberglass repair guy at the marina who said he can fix the problem by drilling a few holes in the top of the cabin, then attaching a Hi-Vac to the lowest hole and over a period of a few days, draw the water from the balsa core. He then pours acetone into the highest hole while the Hi-Vac is still running and draws it through the core to finish the drying process. Next, he pours a very slow drying Epoxy into the highest hole, again while the Hi-Vac is still running. When the Epoxy resin reaches the Hi-Vac he shuts it down, waits about 4 days, then seals the fares the openings. He said the process essentially solidifies that portion of the core that was previously wet, adheres it tightly to the surrounding fiberglass, and does not add a significant amount of weight. No, it's not as good as new, but if everything goes well it should last about 20 years, which is longer than I'll probably be on Planet Earth.
Good luck, and keep us posted on how the repairs progress,