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.
".. 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)
1984 Fast/Nicholson 345 "FastForward"