@Dewster, thanks for your thoughtful reply.
"For the group of 3 pins: the middle pin should be ground, the outer two should be +3.3V. Turning the encoder should cause the outer pins to go to ground and then return high."
The outer two pins go from around 1.9 V to 3.3 V when I rotate the encoder. I guess I am not seeing them going down to 0V, due to limitations of my cheap multimeter, rather than the encoder being bad.
"For the group of 2 pins: one should be ground and the other +3.3V. Pressing the encoder should cause the high pin to go to ground, releasing should make it go back high."
Behaves exactly as you describe.
At this point my best guess is:
1) The encoders are not healthy. I'll try to get my hands on an oscilloscope, and perhaps one of the Alps Engineering EC11 encoder to compare. Or,
2) Somehow in the FPGA re-compiling process etc., the signal read pins got disabled (or something along these lines).
Any of these theories make sense to you? I agree wiring (instead of these more exotic theories) is the most likely issue, although when I double check I think I am matching the PCB layout / schematic etc. I also tried a single encoder on a breadboard in isolation (including flipping some of the pins), but still could not get the display to react.
"And I'm always up for a video call!"
That is very kind of you and much appreciated. I may very well take you up on the offer in a few weeks (once I am back from a work trip, if my debugging is not successful).