Took your advice, Rostin.
FYI for those folks who might run up against this quirk:
When I got the WHG from a previous SEA task, I installed it and then staffed it from personnel I had in my Living Quarters. The task refused to resolve. I 'Dismissed' those personnel, returned to 'Ship Maintenance' and then BOUGHT the personnel to staff the Wormhole gizmo.
Voila! All fixed.
Despite a previous SEA task requiring a new module to be staffed from Living Quarters personnel, this particular tasking required that they be bought and not transferred. That's odd, to me. It did work, though.
the SEA is teaching you how to do stuff. first you staffed a WHG from a LQ (correctly according to your instruction) then when you tried to staff the new one the same way and it did not work. It did not work because you didn't follow the instructions. The first taught you how to staff a module from your own idle crew and the second taught you how to hire new crew.
The voting problem is something else. I thought that just trying to vote (and getting the standard "you already voted' message was enough to pass that part of the course. Did you try voting, or did you just wait until the timer expired? When I was a snot-nosed cadet, I read that advice in the SOL forum.