Ed-
We owned a 1986 C30. I replaced the 1/2" top layer of Marine Plywood due to some rot. It was a miserable job and would have been easier to just replace the small rotted area. The keel stub was quite robust in design. I've attached a note to another C30 owner who was considering the repair. I suspect your 1984 C36 has similar construction, except stringers would require removal- increasing the work effort even more. I would try drilling some 3/4" inch deep core samples and note if the wood is wet or not. If not, fill with epoxy. Replacing the top1/2" layer of the  keel stub wood did not cure the Catalina smile on our C30. I eventually applied numerous layers fiberglass, forming a 10" wide belt in the area of the smile and seam, and fared that to the hull. That , and the re-torqued bolts seemed to do the trick, at least during the three more years of our ownership.

Ed-
I believe the stringers on the C36 boats were used to facilitate the construction process and are not structural elements. but you may wish to verify that prior to any removal. Aside from that, they are convenient to mount things on. Our auto pilot compass,  AC water strainer and manual bilge pump hose are mounted to stringers. 

Also, during winter storage with the mast up, we accumulate rain water in the bilge. Rather than bailing out/pumping the entire bilge, I plug the drain hole in the first stringer and pour a little antifreeze just in that compartment. It makes water extraction easier and keeps the rest of the bilge dry.

Paul