I agree with NZcaver that the simplest solution for the cable ladder is a chest type ascender. Please AVOID using ANY ascender that is attached with a lanyard or tether to the harness. Toothed camming ascenders are NOT to be used for fall-arrest. A dynamic fall onto a toothed ascender can generate enough force to damage or cut the rope.
As for a back-up to the cable controlled decent/accent using the tripod, as LukeM stated, a standard top belay seems best there.
The rope access company that I manage uses ASAPs. We put them on over 4,000 people each year and they work almost without a flaw. But I would never use one in a cave environment. There is too much risk of the cave environment causing a failure of the ASAPs operating mechanisms.
Tim White 26949 RL FE
Southeastern Region Coordinator - NCRC
Editor, Nylon Highway
Senior Technical Manager - Over the Edge, Inc.