Just some feedback on this mechanic--
I feel like it is good to let people know the projected end of the game, but I feel like this prompt is basically a little too aggressive in telling people, 'hey, you need to all gang up on this guy.'
The forecasting of showing the projected winner 4 days out seems a little too aggressive considering how much can change that would dramatically alter the game in that time. It seems unlikely that the game state would stay static enough over that long to actually have that be a set in stone projection. Despite the relative uncertainty of the projection, having someone's name sitting up there probably has a pretty strong effect on player behavior, though.
Two players can be very close to the same projected win time, but one player gets the benefit of not being called out to everyone.
I feel like you could limit this to the last day or two of the game and not jump on it quite so early.