I'm wondering if a 'bed of nails' approach could be used to eliminate the mechanical difficulty of the flying probes? Basically a grid of (many thousands) probes at some resolution, connecting to essentially the same switch matrix backend you already have.
In particular something like [1] might just have enough resolution. The 'probes' now are just pads on the sensing PCB. This converts it from a mechanical problem to a crazy high density PCB layout problem, which sounds like it'd be up your alley!
Heat cure for the anisotropic layer is annoying, and might make it a single-use solution (but that's not bad if you're selling the boards!)
Another 'just dumb enough to work' concept would be to take the board scans, and print a custom PCB of the same pad layout mirrored, and you can directly mount the two boards face-to-face. Basically a board level breakout, either to make the wire soldering easier, or better, again directly incorporate the netlisting hardware.