More wood questions

[Locke N Load]

I am progressing with the demo of my '71 Seafari 20 and, as I am sure has happened to others, each time I dig a little further I want to keep going. This time it is the stringers.

The center stringer I understand is a 2x4 covered with glass. I dug into the end at the transom and it is wet and rotted. I cut back six inches and it is wet and rotted. I cut back another foot and it is still wet and rotted. Is there any reason to keep this wood and stringer? I was planning on leaving it in place as a support for the gas tank. Maybe cut the top off the stringer, dig out all the wood, fill in with foam and re-glass the top?

The next peculiar find was 1/4" thick 2.5" wide by 12" long pieces of wood stacked inside the 4 main stringers at the transom. They were not glassed in, just sitting inside the stringers. Any idea why they would be there? The wood in the two outside stringers was dry, but the the two inside were a little wet. No rot though so it must have been from me making an opening taking out the transom core. I was able to get a few strips out, but not all. Any harm in leaving them in there?