Wow - now there is an application!
Re parallax, yes, that's how these 3D reconstruction programs work. Another buzzword is auto-correlation..
These algorithms have been around for decades and are fairly accurate. I imagine they could be very valuable for your application. There are glitches. For example, repeated patterns in the cliff texture, and protruding branches and roots might fool the software. Also, these are generally designed for horizontal mapping, not vertical, though some of these programs are used to reconstruct radio towers and the like.