I'd be way more concerned about the mushy floor, than the shift bellows---I have a Cobra and I pulled mine off in about 1/2 hr to do the u-joints and gimble inspection, and check the bellows. To get it on is a little struggle but really not hard. There are Merc manuals on line on a couple of websites, try
http://www.boatered.com or
http://www.iboats.com You have to fix that right, or risk water in the gimble area, rusting your gimble, and ujoints.
The floor, well you could be looking at some major work there. I started with a rotted area under the helm seat. Fixed that with a good patch job, then a couple of years later found major rot under the rear seats. Wound up tearing out the deck from in front of the helm seats back to the engine. Had stringers repaired, replaced foam, replaced two 6' long deck sections. Then had the 'glass shop glass it and coat in non skid gelcoat. The inside looks new and the boat is 3x more solid than it was. BTW, FW only stapled the deck down to the stringers with 100s of rusty nasty staples. A thin skim coat of 'glass and none of the screw holes were sealed! And carpet that held in the moisture. I used stainless screws and 3M4200 marine adhesive/sealant. Every single hole was sealed with 4200. Where a fastener had to be made removable, I used threaded inserts into the deck so rot will not start there as it would if you just put a screw into an unsealed hole. No carpet so no held in moisture. I'd never have another boat with plywood decks covered with carpet.
It's not a job I'd ever do again, but this boat is way more solid than any older boat I've been on. More solid even than some new ones I checked out at boat shows (esp Tahoes, the deck on them was really flexy). So much for modern construction!
Good luck with yours, the gelcoat on the outside looks great!