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The measuring coil is a work of genius. It's also the reason why a 1/3HP motor that draws 6 amps won't work on this dishwasher, and a 1/4HP motor that draws EXACTLY 4.5 amps WILL.
From
Home Appliance Servicing by Edwin Anderson:
<blockquote>"Since the measuring coil is connected in series with the impeller-motor winding, an accumulation of water in the machine results in an ADDITIONAL CURRENT DRAW by the motor. When the water reaches a predetermined volume, the current through the motor winding causes a relay coil to open a set of contacts in the water-inlet-valve solenoid circuit, which in turn closes this valve and prevents additional water from entering the washer."</blockquote>
It's ingenious! It's infuriating.

It means that only the right motor with the right current draw (4.5A!) will make this machine hum.
With a 1/3 HP motor in place, the water valve merely clicks on and off, because the constant current draw of a 1/3 HP motor is already more than the system is designed to recognize. Oopsie!
Does anyone perhaps have a 1/4 HP motor that's the old kind (dismantleable), so that I can insert the right end-bell screws? Probably a GE motor would be easiest, but if not, I'll look into getting this one re-wound. We suspect that old GE dryers would probably use the 1/4 HP motor--it'd be too weak to drive a washer (most of those used at least 1/3 HP).
Thank all of you again for all your help! Hopefully we'll get this licked and get back to the world of hurricane-force dishwashing
--Nate