Vince from Cattaraugus Creek Outfitters is taking a DIY trip to Acklins March 1-8. I think the cost is 1650 plus air. He's also a fellow member of this forum.
Feltons runs about 1850 with a vehicle. Of course you'll need food and petrol. His place sleeps 4 which would lower the cost. He can be found at vrbo.com, listing # 49576. Greys Pt also does DIY's Cost single is about 1600-1700 a week. They have a kayak or canoe and would probably rent you a veh also.