I skipped over the majority of the conversation going on here seeing it had no relevance to the issue, so it might have been mentioned......
Have you checked the bushings which house/hold the shaft?, they have a tendency to wear and poor ( cheap ) shafts have a very sloppy fit.
Bronze or plastic bushings, plastic is worse for it, regardless of the thrust washer in place if the bushings are to put it bluntly '
' then your going to get water up the shaft regardless.
Suggestion should this be the case, you may be able to pop out the old bushings and replace, or have new ones machined.
Put a new shaft in, suggest looking at the JP slimline stainless, I've yet to have issues with those.
Or if none of the above work you could pack the shaft with the thick black marine grease ( which i use ) which will stop water ingress regardless of any slop in the bushing(s)