I was there in June and dove with Frenchies. We did an overnight camping trip by the Blue Hole with Frenchie himself and that was great, but I think that is the only trip Frenchie does now.
One problem I had with that Frenchies Dive Shop after the camping trip and we were just doing day dives was that they insisted everyone be out of the water after 40 minutes bottom time and the dive sites they took us to around Caulker weren’t that great.
There is another dive shop that I noticed that looked pretty professional but I’m not certain of the name. I think it had Belize in the title, maybe Dive Belize. I would email any of them you are considering going with ahead of time and find out about their trips.