One way to overcome this situation is by using "magnetically soft" material. Magnetically soft material has atoms that readily reverse polarity (a docile herd?) when exposed to alternating current. Naturally, since the reversing process happens more quickly, there is less wasted energy.
You will need to use the ohmmeter as an ohmeter and not as a continuity checker for the next step in the procedure. You will want to use the lowest ohm scale your meter offers, as the typical winding resistance in motors such as these is less than 100 ohms. If the motor is a permanent split-capacitor motor, you are going to be looking for common and speed taps of the winding.
You should be able to isolate into two groups any leads which have continuity with one another. The starting circuit is likely to isolate to two leads, the running circuit may have two or more leads that show continuity. If the running circuit has more than two leads, you will need to determine how those leads are to be used for voltage or speed changes.
Shield drain wire must be spliced only to mating shield drain wires and not grounded at the junction box. Feedback shields must be passed through pin for pin. Separate junction boxes for power and feedback are required.