Nothing should be adjusted without redoing/rechecking the alignment too. It sounds like a couple of mounts are in rough shape and should be renewed.
If you have a conventional stuffing box then removing the engine and tranny in the water is no big deal, esp if you're able to use the boom and tackle as a hoist. We've done it a couple of times.
If you have a dripless (PSS) style seal than you need to worry about that - once the engine and gear are removed there's no pressure on the seal and bellows anymore....
It does sound like a Re & Re might not be a bad idea, you could tend to these issues, give the works a good clean up, and maybe change some seals and gaskets while you're at it.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)