I know this might sound like too small a change to matter, but it just seems if the game has been going down hill clear to the five minute mark what is the point of a shuffle anyway (a total overhaul of the vote shuffle would be better, but babysteps maybe in order) ? Honestly, I think the 10 minute mark would be better, but chose 5 minutes as more of a compromise.
Problems other than a ton of leavers should have been obvious long before the 5 minute mark and all vote shuffle accomplishes beyond this (maybe 10 minutes??) is a desperate attempt at a win flip by the person calling for it.