Looking at this site for the first time in a long time because we are considering San Salvador next year. To the OP, I am not a diver (hubby is) but I am the trip planner. We have been to many of the out islands of the Bahamas over many years but not for diving. If you are interested in widening the field by a very short distance, have you ever been to Grand Turk in the Turks and Caicos? I took my husband there in November and he loved it. While it was not necessarily "valet diving" as was advertised when we stayed at the Cayman Brac Beach Resort two years ago (so I do understand what you are looking for), Blue Water Divers on GT was right across the tiny "street" from the Osprey Inn where we stayed and the dive boat picked hubby up right there, mere feet from our room, dealt with all the tanks, weights, etc. and kept his equipment at the shop every day after diving until he needed it the next day. GREAT folks and great service. Some days he was the only diver (along with a guide- not extra $ ) and some days it was 2-5 others. The sites are very close and boat rides never more than 20 minutes tops- most about 10. We were there a week and he loved it- I had a great time, too (beach, pool, exploring in my rental golf cart). Take a look.
Also, I have been on the mailing list for Small Hope Bay in Andros for years but have never been- friends have- it is definitely all about the diving so you should look- their website is helpful and they answer their email quickly.
We have stayed at Stella Maris Resort on Long Island before my husband took up diving again- we went out snorkeling on the resort's dive boat- there are some good locations on LI so look at that as well.
There is not really any decent diving around Great Exuma or in most of the Abacos- don't think there is much in Eleuthera either but he did not dive there. Valentine's (on HI) is the only shop around so must not be much demand.
I have done some research on Bimini and the Berry Islands- if you are interested in sharks then Bimini would be your place to look, IMO. Look at Bimini BIg Game Club Resort and the Neal Watson dive outfit.