I do this trip all the time. It's great. They don't get into YFT because they don't go far enough out (although sometimes they will pick up a few). They don't really have a limit on rods, but they don't have storage either. Bring a rocket launcher and store them up top. You really don't need but one, but ideally have three as below.
You need a 40# class rig, on 6.5' rod. I like mono b/c on a partyboat you just have to deal with tangles. Mono is better in this case. I use this for 95% of the fishing, from kings to snapper to BkFT. You can get by with just this single outfit.
I also bring a heavy rod/reel, either 60-80# (usually both), on a 5.5'-6' rod for targeting AJ and Grouper. When you are tied up at night, you can also do a deep drop. Trip I was on last month a guy got two nice grouper this way. I like mono here, but I do not fish the deep drop (where braid is better due to the extreme depths).
Finally, I like an outfit for casting baits, even if I don't do it much. Seven foot rod, with either a spinning or conv. reel, whichever you cast best. Capt does not allow overhand casting on this trip, so I carry a spinner. 20-30#mono is fine, but I use 65# spectra here.
Jigs are primary tool for tuna, fished on the 40# outfit. Pay attention to what others are doing though and switch if you're not catching anything. Sometimes they hit higher in the water column.
Drift baits for kingfish. You can also cast cedar plugs, jigs, etc.
Snapper use lures and/or baits. Use the squid and small hooks for beeliners.
AJ/Grouper use a larger jig or live bait.