Lots of better ideas, already. I like the ripping up old FPC connector idea. Or perhaps you can make your own FPC board, with a large void in the soldermask at the appropriate intervals over the vias. Get a HASL finish. It's sorta doubtful if you could make it reflow, properly with vias that small. You could make them a big larger than the traces and stagger them in two rows. I mean, if it's that hard to get a connection, perhaps you could even make the vias so large they technically touch the traces on either side, and yet it would only connect to the trace directly underneath when flowed? Obviously, you could only do this on the outer set of vias.
Another idea, I have no idea how to spec this, is to make a double sided PFC board with traces that terminate in drill holes and exposed soldermask around the holes. But spec those holes to be plated through holes, so there's copper wrapping all the way around the end of the traces from top/bottom.
But here's another idea:
Might it help to jumper every other trace? Then cover that with a dab of epoxy and a tiny square of kapton. Then go back and jump the other wires over top of that, a little further back? The epoxy will keep those wires from moving (when you inadvertently reflow them making the other half of the connections) and the kapton will insulate the bus wires.
Also, maybe it's possible to use a colored epoxy and a tiny brush (like a cat whisker?) to paint on a soldermask over every other trace that you don't want to bridge?
Overall, I suspect you may have already figured out the best way to do this. Perhaps a microscope and a suitable brush would help in the application of the conductive ink. I believe I read that cat whiskers are the brush of choice for one of those guys that makes paintings on the heads of needles.