Flash has the "inverse square law" issue of light fall-off. The intensity of the light halves each time the distance from the flash increases by a factor of the square root of 2 (about 1.4).
e.g. at 7' you get half as much intensity as you get at 5'. At 10' you get half as much as you get at 7'. At 14' you get half of 10'. At 20' you get half of 14'. At you just keep going.
When you get way out there... 70' is about half the light of 50' ... but it takes a span of 20' for the drop-off to occur. It's the nearby distances where the drop-off is REALLY noticeable... and of course if there was something much closer (say 10' away) then it would get about 30x more light then the object at 50'.
Assuming the cave has strategically placed interior lights (from the videos I can find on the Internet it looks like they do), you might do better on the ambient lighting *if* the camera is on a tripod so you can afford to take a long enough exposure. I'd bring the tripod... assuming they permit those.
Also.... wide angle will work better. You'll see more of it -- and also wide angles tend to "stretch" the size of the space making the interior seem larger. The wide angle will naturally offer better depth of field, but check the DoF and don't cheat it just because you don't have much light. If you're on a tripod and the cave isn't moving (and if it is moving you have bigger problems to worry about) you can take all the time you need to get that exposure. If you cheat the DoF you'll have some stuff in focus and other stuff out of focus and you'll likely be disappointed.
Using a 30mm lens on an APS-C body:
At f/5.6 the hyper focal distance of a 30mm lens on an APS-C body is about 26'. That would give you everything from about 14' to infinity in-focus.
At f/4 the hyper focal distance increases to 37' giving you focus from 26' to infinity.
But if you drop all the way down to f/1.8 the hyper focal distance changes to 83' giving you everything from about 41' to infinity in-focus. If you were to focus closer... say 20'... then you only get 16-26' in focus.
You're basically trying to shoot a "landscape" inside... you want everything in focus from front to back. For landscapes, you normally go to high f-stops to make that happen. e.g. f/11 or f/16.
At f/8 you get a hyper-focal distance of 18.6' and everything from just below 10' to infinity is in focus. At ISO 1600 using only interior rooms with table lamps at f/8, my meter shows the dim room still has enough light to allow for a 1/4 sec exposure at f/8. Judging from the lighting in the videos... they seem to do a fairly decent job lighting up the place... so I'm guessing with a tripod you'd still be taking sub-second exposures at high f-stops.
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