That is a very good question. As you heard in my presentation, my personal preference would be for all committee chairs to be elected on the same day. Effectively we would get handed a stack of ballots, and away we would go with the ballot boxes and vote.
However, if the committee is open to the idea, perhaps you could stagger it week after week. You could have perhaps the 10 most interesting committee chairmanships the first week, the next 10 the week after, and so forth. Or you could have eight, eight, and eight, because I think we have 24. There are all sorts of options for the committee.
In your first question you asked me if I'm mostly interested in the principle. The answer is yes. I'd be interested in and open to either solution.
My personal preference would be to vote for them all at once: you take your chance on what you want. I can see, though, that some members would be interested in having perhaps eight go in one round, eight go in another, and finally a few more in another round. That's an option too. If the committee can arrive at consensus one way or the other, I'd be fine with that.