I recently encountered similar experiences in one of the ND caves (Wind). Fortunately in my case, low-level incandescent lighting was provided along the way because I was on a guided tour; I brought my flash in but never used it -- it just wouldn't have captured what I saw, and since I was on a tour I didn't have time to set up anything usefully creative anyway. I had to shoot quick, look for opportunities to rest the camera on something like a handrail, utilize wide apertures, IS, and got few keepers.
I had a lowepro sling so I could change lenses without taking the backpack off, and utilized the IS WA most of the time (17-55). I got my 70-200 f/2.8 out just because I wanted to, and got a couple of surprisingly acceptable close-in shots of some features by resting the camera against a handrail. next time I'll bring a monopod. In my case, a tripod wouldn't have been practical; no time or space for set-up.
if you are not on a guided tour, and you really do have the time and space to bring in lighting and tripod, all the better! its just that a single, straight-on flash won't capture what you really see. without installed "tourist lighting" already in place, and with the time to be creative with a tripod, I think I would be tempted to experiment with "painting" light manually with shutter open -- assuming you have the time of course, and freedom to move about the cave. For example: open shutter, paint light, then move to another location -- paint more light, lather rinse repeat, then close shutter. remote shutter release would be useful. Another alternative, if you really have the time and freedom to be creative, is to place some flash slaves strategically around various places.