So today I had a more determined effort. I shifted all the anchor chain and much of the ballast onto the starboard side deck. When Bonita floated on the spring high tide I rigged up a rope from the mast to a post ashore, and tightened this up as hard as I could. The net effect of all of this was to give her a gentle list of a few degrees to starboard, about as much as sailing in a gentle breeze. It didn't seem like much but it was enough. When the tide went out and she sat down in the mud, the shaft log was just visible. It was relatively simple to slide in the new shaft and propeller and connect it up to the engine.
Its important to keep a line attached to the new prop while installing it as the shaft and prop are heavy, slippery with mud and expensive! The mud is so soft that anything dropped in it is likely to never be seen again. I had been worrying about this job for a while so I was relieved to have got it done. It should be a few weeks before we take her out to her mooring on the Swale to start the new season, but all the remaining fitting out work should be (I hope) fairly straightforward.