If you want to stay at Sapphire, there are four "properties." They are all condominiums. The least costly would be Sapphire House, but there are only a few units there and a rental would be difficult to impossibly to find. The next best bet, would be Sapphire Village. The big, and possibly drawback is that there may be A LOT of stairs to climb, either to the beach, or to the road, or both..
Off-season is an excellent idea (as with most places). Some places drop their rates at the beginning of April, some in mid-April, Some at the end of April. In any case, the weather (and everything) is just as good in May and June, as when the rates are twice as high.July it's just beginning to get a bit hot but it is a popular month for owners. August it's pretty hot, and the end of August you are getting into the beginning of the peak hurricane season. Don't forget that even if renting a condo from an owner, there is a ten per-cent "hotel tax".
Don't forget to allow for on-island transport. If you rent a small car, figure just about fifty bucks a day total. There are other methods of getting around, but a car is a real convenience.
Finally, and probably most important. If renting any condominium at Sapphire (and probably any on island other than Secret Harbor) it is extremely important to rent DIRECTLY from the owner. Just look for units that have a lot of favorable reviews on the VRBO/HA listing and /or TripAdvisor.
As an example, "KB80439" used Expedia to reserve a unit.