Marinas or Anchorages Near to the Exumas

He said Cave Cay was too far, not EYC.

I tend to defer to the collective wisdom on this site. But the Exuma Yacht club was in shambles last June. No way would I leave my boat there whether I stayed on it or not. I would take my chances at Emerald bay and double my lines and put out a lot of heavy duty fenders. I wonder if you were to get a slip to the far right on entering if the surge would not be as bad there. Another thought is to see if St. Francis Resort would have a slip for you. There was an 80’ in there last June. If you draw 5’ or more I think you will have to time the tides but once in I think it would be fine.

And what do you do for things walking off your boat? There are reasons you don't want to leave you boat at most places.

Right? How do you leave the boat anywhere without someone responsible aboard and in charge?

Even in Marsh Harbor, Boat harbor, Elliot & Treasure, in the good days, I would deliver a boat and within days when the owner arrived, stuff had walked.
One owner found his scooter, removed from the cockpit in the marinas parking lot when he arrived. Of course, nobody saw a thing.

To answer your question; IMO, You don't..

It does amaze me that many people do (did) come back with no issues.

Well, a plan for everyone and to each his or her own.

Given the likelihood of trespass and the frequent brown outs, no, it's easier and cheaper to have a reliable steward aboard in the vacancy.

...oh, and I suggest that since you will be leaving her alone as before that you place a small cup of water in the freezer, let it freeze, then put a coin on top of the ice inside the cup. When you return if the coin has sunk into the ice, throw out your food.