I tried wiring the motor similar to what was shown in the 2nd diagram even though it's basically a 4-wire motor instead of 6 (2 posts for the blue & yellow wires and 2 posts for the black & white wires).
Since I don't have the dpdt switch mounted in an electrical box yet due to trying different wiring schemes, I would first position the dpdt switch to one of the 3 positions and then plug it in. The motor did seem truly off in the center position (no humming), and reversed direction when the switch was in the other 2 positions. However, the motor did not consistently spin in the same direction each time it was plugged in with the switch in a particular position. Sometimes the up position was forward and other times it was reverse. Occasionally it would not turn at all and just hum. The motor also seemed to get very warm rather quickly.
Not sure what's going on at this point or why. It does seem that the dpdt switch cannot provide the directional switching and off options for the lathe like I was hoping and a drum switch is needed to do the job.