Sure. I don't believe the situation is so dire that we can't take the time to do it properly.
Choosing someone who's partly inactive or semi-active when the need for a active global moderator arises is counter-intuitive.
This remedy still requires all who already voted to notice there was a change and I doubt people are going to keep checking the thread when it bumps since that happens every time there is a vote.
There's plenty of time to fix your vote. I'm pretty sure that the error rate would be marginal in the end.