Actually, Marsh Harbor (MH) is a ferry and taxi from Green Turtle. However the Green Turtle (GT) / Treasure Cay airport is closer. Still a ferry / taxi but less in taxi. Prices vary as to Airfare cost. Once couple told me that flying from BU to Nassau to the Abacos was 1/2 of going through Fl. Lots of ex pats in the Abacos leave their car at one of the commuter airlines in I think West Palm. Cars were left free there. The yard in GT is excellent and you'll actually need to see if they have space and make a reservation. I think once you're in you'll be good to go.
Of course you can get a yearly mooring in one of the sounds and and Black Sound is quite full of them. I would suggest you take some of your own care of the mooring as I know personally of two boats that broke off the mooring (one a cat had so much damage they had to go to Nassau to haul because of their beam) and they had significant damage, the second a mono broke off the Green Turtle Club mooring (still had the mooring ball and chain attached) and ran into a dock with a boat on it ashore (no real damage there). A sailing fiend we met there when they went to put their boat on the mooring dove on it first. Found the shackle almost corooded through removed it and got the owner to replace to give him a new one to replace it with. The mooring owner said "Yeah, I was planning on diving on it to replace it soon". Funny how that is.
Can't tell about other yards. There is some mooring storage in Man O' War. Don't think there is much on the hard there. A good yard in MH but I don't know about storage there either. Scott is the guy in GT.
Fair Winds