Took out the PCB and wired in some nice cables. The solderings look nice, so I'm not sure what could be the problem. And, as it turns out, there is no problem The PCB is perfect. But when I put it back in and measure (without the motor or Melzi connected, there's connection between black and green, between black and blue, and between green and blue.
Rechecking the male and female D-Subs, the female does indeed show connections between pin 15, 7, and 14. I must have held the cable just wrong when crimping it. Sadface.
After checking carefully that pin 8 of the D-Sub is not used, I decided rather than wait to get a new one, I would cut the last 5 wires off the flat cable and connect them directly. In order to make it be disconnectable, I wired them up to male/female single connectors, like this (but with some tape to keep it from getting entangled in everything):
With these connections in place, I should be able to run the extruder. Aaand... it stutters:(
To debug this, I first switched back to direct connections, then one cable at a time to the flat connection. Already the first one (red) broke the nice, smooth extrusion movement.
Looks like the wiring wasn't quite as I saw it. The flat-cable wire I thought was blue is actually red. Which means I've cut some unrelated cable, possibly for the fan since both heater and thermistor works.
Finally got through all the wires and it now extrudes with the correct connections and nicely taped up.
Added some filament and did calibration: Started with a mark at 100mm, then told it to extrude 50mm at 60mm/min. Afterwards, the mark was at 67 mm, so it extruded 33 mm instead. Important difference.
Here's a bit of extruded filament hanging down, as proof: