The drive shaft rubbing the shaft log is a big time sign that the engine is out of alignment. (And this caused my boat to sink once.) Here's what I would do to start: Check engine mounts. Are they solid? Pull out a few of the lug nuts and see what comes out with them. Clean/dry wood or black mud? If there is mud -- you're screwed. Stringers are shot. If there is some evidence of solid wood -- buy a lottery ticket, get some slightly larger lag bolts and secure those buggers. Then you can move on.
Next step is to pull the coupler, drive shaft, and strut. Strut and drive-shaft should be checked for straightness and repaired if they are out of spec. Both should be able to be checked by a prop servicing facility. Looks like you are in IL? Someone may have a recommendation for you.
Now -- in the event that your stringers are shot, you'll need to do some work to see just how shot they are. Without a doubt, you'll want to start by pulling the floor and removing as much of the really gross wet foam as you can. Then you'll want to drill some test holes in your stringers to see just how far up they are rotten. Knowing what I know now, I believe it's easier to pull the entire cap and replace them in their entirety -- but when I did the job, I didn't have the expertise of the forum and did exactly what you are describing -- I only replaced my stringers from the bow back as the ones in the front were still solid. In hindsight -- I believe that this was more work/effort than just pulling the cap would have been.
Sorry if I'm the bearer of bad news -- but -- it's (most likely) going to be a little baptism by fire. Good luck!
Former owner of a 1987 Supra Saltare. Current owner of a Malibu 23LSV.