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.
Modern portable devices often have BGA packages with 0.5mm spacing. At this resolution, a relatively small 5x5 cm board would require at least 100x100 = 10k probes per side. Count increases quadratically with board size.
Far easier is a "flying probe" machine [1] with a handful of probes that can be moved quickly. This option is mentioned in the article, but dismissed due to up-front cost.
You could multiplex the probe grid along rows and columns like pixels on an LCD screen. Would make the probing take a bit longer but you'd still save time since you don't need to manually hook stuff up.
I'd just solder paste and reflow, like a large surface mount device. Challenging to get consistent no doubt, and the alignment would have to be very accurate (or have a few separate boards), but I think doable.
Seems like you could largely automate a workflow for identifying pads in the scan and generating the mirror layout, with simple routing to some kind of standardized interface for the probe lines.
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.
[1] https://www.3m.com/3M/en_US/p/d/b5005076018/