Out of your suggestions, this would be the one I'd go with.
Although originally when I had pictured it, I thought each mod/candidate would get their own thread/poll. That was before each got a Q&A thread. And people could either support or not support that person, and the people with the most support would be the ones to get the green light. So idk if that would be a thing you'd want to do.
Oh and private. Definitely should be a private vote.
Quick question about this. Two? or three? Cause I couldn't help but notice Force put into the Retired Staff category. With Tenny & Force gone, you'd have to fill those two, plus the one you wanted before any of the staff left. idk if you feel like you need that many, but just asking.