You want lots of strobes, but you can start with one or two. I would recommend starting with one powerful one (like the Z330) and then buying more of the same as you can afford it. There are advantages to having a matched set...I have six Z240s that I use off camera in the caves. More than two strobes per diver/model plus two for the camera is usually overkill, depending on the cave you are in so that gives you an idea of how many you might end up with 
If your budget restraints are significant then perhaps a set of used Z240s might work for you? I would only recommend them if you are diving in water colder than 25 degrees, as they are more likely to be on repeated full power dumps (and thus overheat and burn out) for cave diving. The Z330 supposedly has an overheating cut out in it.
You might find some interesting effects from combining constant and strobe lighting as well. One issue will be that the strobe is much brighter than your video lights, so if you put the strobe on the camera and the video lights on your models then you may wash out the video light. The light drop off in water is why it's better to put more light on your models (as in, light source attached to them, not you). Then a little bit of light on the camera for triggering and foreground fill, and big bright strobes on the divers to light up the tunnel.
Lastly, embrace the darkness. Caves are dark. If you light the whole thing up like daylight then it just looks like a pile of rocks. Show off the mystery in your photos by working out what to light and what to leave.