Less pictures of the motor, as OH didn't want to be photographed mid-solder!
This was the state of the wiring to the motor before
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OH cut the wires away at the broken points, and spliced in new wires, each one soldered. Then fairly long insulation sheaths were placed over each join, and the original outer plastic-y sheath slid over the whole lot (we softened the outer sheath in just-warm water to uncrankle it a bit). This is the finished result, you can see the kind of insulation sheathing he used next to the motor.
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Then we jury-rigged it via the machine socket (using a safety cut-out plug to the main) to check that the motor now ran. Success!
The worst part was that the grease ports on this motor had been filled with a dark heavy car grease - and REALLY filled! OH says it was probably done with a grease gun. We had a bit of trying time getting it all out - it squeezed/squelched out of the holes like . . well you'll have to imagine what it was like, but it had to come out. We hope no permanent damage will be done to the motor that some is inevitably remaining. I have now used the correct grease in the ports.