Some updates in case anyone else comes across this thread:
As soon as I took apart the membranes, all the traces near the edges started flaking off, and had to be redone. And while I was able to get keypress events shorting the ribbon connectors with a 200kΩ resistor, it turned out that even around 15kΩ between the ribbon connector and key pads was too high to work reliably, possibly due to additional resistance where the conductive surfaces from the two membranes press together. This posed something of a problem because I'd figured I had a bigger resistance margin to work with and hadn't optimized my conductive paint for low resistance.
In the end I managed to get all of the traces below 7kΩ, and most below 3kΩ, and the keyboard is working great again now.