The newest stereo cameras have done most of what I was hoping to accomplish here with this project. It's not super-cheap, but it can be run on next to any source since it has onboard processing.
I've just started playing with mine, but so far it was cheap enough that I grabbed 3 Oak-Ds just in case I could get them to work for a project.
While I still think that 2k cameras aren't enough for pure-stereo vision with quality depth, hopefully the powerful onboard controller chip (the Movidius-X, the same chip in the Neural Compute Stick 2.) may allow for enough processing (including AI) to make the depth signal high quality and clear.