He does exactly what you are thinking of, only he does it in the Med, instead of the Bahamas.
Over time, he has found a yard he prefers to leave it at while in the states and seems relatively at peace with the whole situation.
Surely somewhere in the Bahamas, there is a yard that can be trusted with your boat. Failing that, I have several friends who have left their boats at a yard in Marathon, between jaunts to the Bahamas.