Also haven´t found Caribbean islands where beaches come even close to Eleuthera Mind you haven´t been to Cat island or Great Exuma yet.
I would agree with previous poster that Anguilla could be an option but you will not find beach villas in different price ranges as in Eleuthera. Villas are mostly ultra luxurious types with prices per night starting from what you will be paying per week in Eleuthera. There are some choices of more affordable accommodation in condos or hotels though and if you are not set on private villas with beach which sometimes feel it´s your private beach I would definitely give it a try.
Seychelles are beautiful ,been there twice and stayed on 4 different islands with Mahe ( the main island) in my opinion having the best choice of beaches of all 4 I have seen. Again, difficult to compare with Eleuthera beaches, their beauty is in dramatic set up and background of enormous boulders, rocks and vegetation. Beaches are rarely isolated, but far from crowded. Would definitely recommended it , but try to stay in private accommodation to get peace and isolation you want.
Cook Islands as ChicagoBear mentions have beautiful atolls but I personally didn´t find them so great to be willing to suffer long trip there again ( from Europe). For me Maldives are much easier to get to and provide similar kind of atoll beach experience. For my next Pacific islands holiday I will try toe get at least 3 weeks of work.
I personally haven´t found another Eleuthera yet and have been to quite a few islands around the world. But search is not over yet ;) As I normally try to have two long haul holiday every year I have decided ( since I fell in love with Lutra couple of years ago) that Eleuthera will become my yearly staple destination, leaving me the second trip to go and try different location .
Happy exploring and do let us now if you come across another Lutra.