Hi Jane,
We were there in 2006 (maybe 2007?) Beautiful island, much more undeveloped & "deserted" than St. John, and really lovely secluded beaches. Eleuthera is flat & scrubby and doesn't have the hilly lush beauty of St John, though. Also doesn't seem to have the infrastructure (although maybe we didn't explore), but for groceries, there was nothing like Starfish Market, for example, and the rental cars were...ummm....well-used!!

I don't know exactly where the house is, but it sounds like it's up not too far from where we stayed (in our pre-villa days), at a resort called The Cove. We never made it over to Harbor Island, so I can't speak to that.
If you go, I definitely recommend getting the book "The Elusive Beaches of Eleuthera", because some of the most gorgeous beaches really are seriously hidden (like a "This isn't a road...it's an overgrown dirt path that nobody's used for 32 years!" kind of hidden).
I was pretty disappointed in the snorkeling, and the water was chilly, but I think that's because we went in April.
One memorable moment was bumping into Lenny Kravitz on a deserted beach (there were four people total on the entire beach-- me and my husband, and Lenny and his friend). Crazy! I was too shy to talk to him, but my husband asked if he knew where any good snorkeling was. Lenny flashed his rock star smile and said he really didn't know.

I didn't ask him if he was gonna go my way.
It's a low-key, charming island! Still, since we discovered St. John the following year, we haven't considered going back because we fell hard for STJ.
Happy to answer any specific questions!