New secluded places

My wife and I try to take a trip by ourselves to the Caribbean once a year. The older we get, the less we like people and tend to look for very secluded places. This past summer, we spent a week on Guana Island, where we felt like we had the island to ourselves. Now we are hooked. I was wondering of other people’s experiences with similar locations in the Caribbean. It doesn’t necessarily have to be an organized « private island » with all inclusive or anything like that. Just somewhere where we will feel like we have the place to ourselves. I’m currently looking at Anagada (the Settlement) in BVIs, and it seems to be exactly what we like. Somewhere we can where we can be by ourselves and explore the island and beaches without a lot of people around. Has anyone stayed here specifically or it does anyone have any recommendations on places like this in the caribbean? Thank you in advance.