So, by reversing the leads you mean you connected the shield/ground from the pickup wire to the lead of the jack? Or you had it all wrong from start and now you correctly wired the shield/ground to the ground of the jack? Or is it that the wired from the pickup is not the shielded type?
I had the pickup wired direct to the output jack - so I just reversed the leads. I originally thought I had the wrap wiring to the jack tip and the shield to the shaft/ground, but evidently not. Reversing them eliminated the hum.
This feels like the Homer Simpson moment: "D'OH!"
Next step was to re-connect the 'bucker pickup wires to the control pot, but reversed from the original (humming) configuration. Then the output of that control pot and the other one were connected to the output jack. No hum!!
Dave, Yay is both highly appropriate and a massive understatement. Thanks to ALL of you for hanging in with me and providing such great suggestions!