I was on the Bahamas Aggressor the week of November 23-30, which would appear to be the week before the OP's trip, if I am not mistaken. My take on the whole experience was similar to that of the OP but a bit more favorable: the boat and the crew were good, but much of the diving (with a few key exceptions) left much to be desired. I normally write a full trip report, but I had so little to say, and the OP had already conveyed the gist of what I would have said, so I will just add my comments here.
I had originally been hesitant to book this boat because of some extremely negative reviews in years past, stemming from major mechanical problems that disrupted diving. I was relieved to learn that they seem to have fixed these problems, except for some low Nitrox blends on one or two days, for which the captain reduced our Nitrox fee by half. Yes, the boat is old and small, but I did not find that either of those points detracted significantly from our experience. In fact, I would argue that the somewhat smaller number of guests made the experience more enjoyable than it might have been otherwise, as we had a good group dynamic. The crew was professional and attentive – no complaints there. The food was good, which seems to be par for the course for Aggressor boats.
I found that the most interesting dives were actually the ones closer to Nassau, including the very shallow and very beautiful Periwinkle site that the OP mentioned, which we also did on our last day. Also of great interest was the Blue Hole, where we saw a “sharknado” school of reef sharks inside the hole and a lot of sharks, rays, and other fish near the coral heads and sea grass beds around the mouth of the hole. Also of particular interest was the wreck of a drug smugglers' airplane that crashed in about 20 feet of water and was teeming with schools of fish and many macro critters. The downside of these sites, which seemed to have a greater number and variety of animals, was that the water was colder and the visibility was lower, which was a reasonable trade-off for me but might not be desirable for others. I am now curious about what it would be like to dive with a land-based operation out of Nassau, such as Stuart Cove's. This would have been a better trip if most of the dives were like these.
The highlight of the trip for me was the two shark dives on the Austin Smith shipwreck. Sharks are arguably one of the main attractions for Bahamas diving, and I certainly got my fill of Caribbean reef sharks on these two shark dives. As for the regular dives, we did see Caribbean reef sharks more frequently than we would in other destinations in the greater Caribbean, but not as frequently as I would have thought, given the Bahamas' reputation for sharks. I found that the Turks & Caicos actually had more Caribbean reef sharks, if you factor out the Austin Smith shark dives.
Once we got into the actual Exuma Cays, the reefs were not in great condition, as the OP wrote, but steadily improved as we approached and eventually entered the Marine Park. The Marine Park did make a significant difference at least in the health of the reefs. What disappointed me more about the Exumas was the scarcity of moving animals, aside from the occasional shark, lobster, or lionfish. On that note, the lionfish infestation seemed to be worse here than elsewhere in the greater Caribbean, as I saw them in greater numbers and larger groups than I have anywhere else.
I would be willing to go on the Bahamas Aggressor again, but I would not have any interest in visiting the Exuma Cays again. I am curious about the boat's other itineraries, particularly the Tiger Beach itineraries, but I was wondering what if anything I might hope to see on these itineraries other than sharks. I am also curious about the diving closer to Nassau, where the conditions might be less desirable for some but seemed to have a greater density and diversity of moving marine life.