O.k. I have opened the voting thread here
I have decided to have a public poll. But, as a compromise, members who would prefer to vote anonymously are allowed to send me their votes via private message. Each voter can vote for as many individuals as they wish.
At the moment, I think it's best to have a single poll. Based on voter turn out and how close the race is in this poll, we can then decide whether we need subsequent polls.
Thanks again to everyone who has agreed to participate, and to all of the feedback regarding this process.