Peter - I found the moisture meter readings to be very reliable on locating the "boundaries" of moisture. The one I'm using is a JRC with traditional analog meter that I borrowed from a friend who is a Marine Surveyor. Like you I found the only good way to see if the balsa is rotted is core samples.
I also found rotted core at the top of the transom on stbd side. My plan is to inject the upper inch or so with thickened epoxy to isolate the new balsa I'm bonding in. The seem between the transom and rest of the boat will also be setup so the balsa is isolated on both sides.
It's interesting that your outer skin was thicker. Mine was like paper, so before bonding new core I've bonded two layers of 17oz biaxial fabric to strengthen the outer skin. Take pictures - you can see some on my blog at this link:
http://j30rhapsody348.blogspot.com/ although I haven't done any work in a couple of weeks. I wish I had the inside work area you had! Mine is being done outside and I will tape fiberglass insulation to a section on the outside, then heat from the inside before doing any bonding work.
On a different note, I just got my rebuilt prop back from Martec. They rewelded the stops, overdrilled the pivot pin hole, machined new edges and polished it like a mirror.