I... don't really think so XD You should talk to Live Wire since he's the one in charge of Other Chat, but all those contests are usually run or at least endoresed by the staff so we can monitor such huge votings so I don't know how it would go if you opened one right away.
No, I'm afraid we don't have any of those here. Although there's a discussion about restarting Poll of the Week in Other Voting Polls, that's kinda similar.