Thanks everyone for the comments, both on the thread and through PM. I bought an 8oz ball pein hammer and got a bad dull thump all around the area in the photos with the cut marks. I also bought a cheap MMD7NP Moisture Meter because that is the only meter that was available in any store around here. Realizing that moisture readings are very susceptible to the method, I tried all four mode settings on the meter and they all defined roughly the same exact moisture area right around the markings. The area is about 18 inches horizontal by 6 inches vertical.

The source of the water wasn't hard to find: the bilge had a lot of rainwater which probably came in from the mast which was never dismantled prior to two years of being laid up (pic attached). The starboard aft quarter corner of the bilge has the lowest run off drain (given the current storage angle) which perhaps is supposed to run aft but if so, the channel is clogged forcing the water to run off to the starboard quarter aft storage compartment where it pooled up and eventually soaked through into the core (pic attached). As the temp froze and thawed over the past two years, the wet core eventually expanded and broke through the gelcoat in the exact location of a prior repair from what I would imagine was exactly the same problem.

That's the situation, now its time to get it fixed so that I can be out on the water instead of pacing the yard!

I've found some decent links to help guide a self-repair:

http://epoxyworks.com/index.php/common-errors-in-fiberglass-repair/

http://epoxyworks.com/index.php/replacing-damaged-balsa-core/


Here are my questions/concerns:

1) The repair quote I got over the phone was $500 per sq foot. I'd imagine the cutout area here will be around 3 sq feet, so a guesstimate is about $1500 which seems low given the costs I've seen by browsing the web. I'm leaning towards doing the repair myself though since it seems a small enough area. The boat is outside in a yard that is 100+ miles from my house, so I have to do this work in a yard without power and with the tools I can fit in my car.

2) Perhaps it is fortunate that the water found a quick way out and does not seem to have caused more damage. Which makes me wonder if I do a 100% job on this repair, where will the water go the next time this happens? Perhaps if I clean out all of the bilge drainage channels, I won't have to worry about it. But since this is the 2nd time this has happened in the boat's lifetime, I don't want to create more of a problem than I am fixing.

3) It doesn't seem like it is worth it to dry out the core using a vacuum and/or heat application. The outer shell has been compromised, so the core is most likely contaminated and rotted, and will have to be replaced. It is hard to imagine there is any structural integrity left in the balsa considering the sound of the tapping report which sounds similar to tapping mud.

That's really it. If anyone else has any advice, comments or links to help me on my way, it is greatly appreciated. Thanks to Chris for recommending Don Casey's book which has a good description of the recoring process.
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