The Turks/Caicos boats (Explorer or Aggressor) might be an option. I did 25 dives on the Explorer a few years ago and sat at least one out - maybe 2.
Direct flight from Charlotte to Provo (PLS), a crew member will be waiting at the airport. They'll shuttle you to the boat - or drop you for lunch then your gear to the boat - there's typically a 2nd later flight in.
They dive a few days around Provo then move across the channel to West Caicos for deeper wall diving. You don't have to do it - I solo'ed quite a bit and 60' is my max for that - I don't feel like I missed much. The last stop is French Cay which has to be one of the
naturally sharkiest spots (including the Bahamas) that I've ever dove. Every dive there were several - sometimes more than that. Plus I counted 24-25 Stingrays on one dive - most while doing a safety stop near the mooring.
I spent 20mins. of one dive filming the interactions around one coral head - the baby fish, feather dusters, small invertebrates that all lived on it. There's no real wrecks though - just a small plane we didn't look for and an encrusted engine block that fell off a boat. You also do a couple of drift dives in one area.
Nice boat, good crew - we chose the Explorer over the Aggressor solely based on price - took advantage of a $400 discount on a spring trip. Several times the Aggressor was on the next mooring over. Our boat had one extra deck (covered flybridge with seating) which meant the majority of cabins were main deck or above - Aggressor's are all below deck. Big room also, two twins, small end table - a 4' desk in one corner and a decent sized closet IIRC - even 2 windows (not portholes). The only bunks on Explorer are the 3-4 below deck cabins and they're ensuite also. It's not a new boat but the crew told us it was originally built as a liveaboard - not converted from something else. Even the bathrooms were decent sized.
Year of Savings Specials - Explorer Ventures - might find something that works for you.
Also both boats do whalewatching at Silver Banks from about Jan-Apr - no diving.
Besides all the options listed at aggressor.com - here's a few other boats I haven't seen mentioned yet. All are Bahamas operations afaik.
Cat Ppalu - same company as Blackbeards.
Lost Island Voyages
Dolphin Dream
I saw the Cuan Law once - it's huge - dwarfed our 45' dive boat. Plus the whole deck between the hulls is for hanging out.
I'd rate the diving in the B
VI's maybe a step down though - although it might be a good option for you being shallower - there's not a lot of depth anywhere. The Rhone is a good wreck and there's a small wreck alley - one natual the rest placed. Most dives I don't think we broke 60'. What's nice about the BVI's is they're an hour ferry ride from St. Thomas - which has lots of Saturday flights since it's a cruise port.