I don't think you're going to really effectively dry out that plywood in any reasonable period of time. It has probably taken a long time to get this wet, and would take a really long time to dry, especially with only one side exposed. IMHO, you'd be better off re-coring the cabintop. Marine plywood is the worst of all core materials for cored laminates, as you can read about HERE
If you do decide to recore the deck, it would be my recommendation to cut the top laminate layer away rather than try and do the work from the underside. Working from the top will make the repair go much faster and gravity will be working with you.
Working from underneath will require you to mask off the entire interior and will make it much more difficult to get a good layup without voids. Finally, any bulkheads are going to make getting the core repair more difficult to do.
Finally, I'd recommend using end-grain balsa or a ductile polyurethane foam like Divinylcell. While a rigid foam might be better, it would be harder to work with. For end-grain balsa, something like ContourKore, which is designed to allow the material to follow fairly complex curves, rather than solid sheets of it, would make laying up the new core much easier.
You should probably plan to make the areas beneath major hardware solid laminate, rather than cored laminate, and any smaller hardware that is mounted through the cored areas of the deck should have the fastener holes potted. To do this properly follow Maine Sail's excellent directions
I'd also recommend you read my article on marine sealants
prior to rebedding any deck hardware. One of the most versatile and effective sealants is Butyl Rubber Tape, which you can get at many glass repair shops. Not only is it very useful for bedding all kinds of deck hardware, it is also very inexpensive compared to other marine sealants. However, I would not recommend it for below-waterline use.
We noticed that there was some coffee-like liquid oozing from a seam on our Cal 27's cabin ceiling. So we knew we had a soggy deck, though it doesn't feel spongy when walking on. The boat cabin isn't lined, and there isn't any paneling or furniture in the way, so it is easy to access the deck from the interior. We cut out a small section with a dremel tool, without going through to the top. The construction of the deck is, from the top to bottom, gel coat, fiberglass layers, plywood, fiberglass layers. The small section we removed revealed that the plywood was damp but does not appear to be rotten or mushy. The plywood was still attached firmly to itself and both layers of fiberglass. So my problem is -- how to effectively dry out this plywood? The area that needs to be dried is large - I think the moisture wicked along the wood grain, from a leaking chainplate nearly back to the companionway. I expected the plywood to be rotten, but it is quite firm and we really had to pry/chisel it off, though it is clearly damp.
So, I am thinking we can pry/peel away the inside fiberglass layer, and attempt to dry the plywood from underneath using a heater, but I don't know if this will work, as the water vapor cannot escape upwards without putting holes in the deck surface (which I'd rather not do).
Anyone had any experience with this, or any ideas?