I got the expected results using a 100W light bulb.
With the assumed correctly connected phase (using an inline meter), the light bulb was off: 120V AC using a VARIAC, 203mA, 17.75W, 0.741 power factor.
With the assumed incorrectly connected phase (I was too afraid to go higher in voltage) the light bulb was on: 30V AC using a VARIAC, 413mA, 12.5W, 1.0 power factor.
Afterwards, knowing red to red and black to black was correct, I hardwired all the wires, reconnected the connectors, etc... and tested the power supply. As expected it turned on, but I didn't do a load test yet (unfortunately the only adjustable load I have is a single channel 180W variable load).
A few things baffle me about this experiment. Initially I used a 60W light bulb and it was on when the wires were wired correctly. Was this due to the resistance being higher in the filament?
Also, I don't comprehend how wiring the two primary coils out of phase causes a short whereas in phase they keep the bulb from turning on.
In phase and the two coils are in parallel. Initially I measured (rounding off) 1 ohm on both, so it would be 0.5ohms and would think the bulb would be on due to the low resistance in series with the bulb.