Chasm (Cave 7) Need advice

[AcidMantis]

So I'd like to cross Cave 7 off the list. I spent a while carefully clearing out the main chasm area, from the modern axe all the way to the 2 Virginias. I went past the Virginia room into the "L" shaped room with all the stalagtites and a couple hanging bodies, and the cave painting of the big red man. I turned back because I wanted to save and had a temp. shelter for saving up by the modern axe. On the way back, I found the wood barrier in the Virginia room, and located the bomb wall, but I had used em all on Virginias. I don't have the climbing axe yet, so I don't think I can get back out of the tennis racket/pedometer area.

Does anyone know what I have to do to clear it? Can I just get the climbing axe and clear the tennis area, or should I also blow up the bomb wall and go that way? It sounds like there is an Armsy past the "Red Man" painting too, so that makes a possible third area I need to do. Do I need to clear all of those areas, or do some of them count as parts of other caves?