Attempting to avoid the problems from last time, I soldered all the wire ends going into the Melzi before wiring the old board up again. Well, half of them. The other half were hiding so well I missed them until wiring time and then didn't feel like going back to soldering.
Add power, and all systems are operational (though some wired a little funny)! Woohoo!
Removed the new Melzi and re-mounted the old one. No thanks to 3dnielsen.dk for still selling the old 10K ohm version of the Melzi.
Tried connecting through the normal wires to the extruder motor. It reacts, but stutters rather than move, probably some connection is bad. I can now either try to fix that or try extruding something. Since I have little time left tonight, I certainly can't extrude something real, but I can try feeding some filament and adjusting the potentiometer. Here's how to adjust the potentiometer, not too difficult.
The resistors say R110, so that's .1 ohm. My motors are of two different kinds: The extruder motor came with the extruder, while the other three came from elsewhere. So quite possibly the extruder motor needs a different amount of power.
But I'm running out of time for today. Maybe over the weekend I'll have a longer stretch of time. Especially if that Civ game doesn't get more players than have replied so far.