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I was actually thinking an access panel might not be too noticable. Fairly sure it's a lath ceiling up there somewhere so lots of potential for it to be harder than you make it sound. Had a feeling that setup would bite me at some point. Going to sand the patch, and keep an eye on it for a bit, doesn't actually seem that damp, could just be a coincidence...🤞
Polygon-
I've done it with lath but lined the whole ceiling afterwards. It was a bathroom under an en-suite shower. One of the copper pipes developed a pin hole leak (usually from iron deposits in the copper). The leak went into the bath underneath.
You could use whatever you cut out and fix 6mm moisture resistant mdf to it to make a hatch, you would need to find the joists though. How often does anyone look at the ceiling anyway :)
Airhead
Or just cut the patch out and tell anyone who notices it's a maintenance hatch which is a requirement for showers since new regulations came in :)