I almost always prefer full press to public press, so I'd prefer PM's. I'd imagine a public press only variant would end up being far too chaotic if everyone was involved.
I also think you should drastically reduce the number of possible coalitions, but perhaps after balancing them there will be reason for there being so many.
This one is huge:
Players should not be able to freely give other players points. At best there should be a limit on the number of points, or perhaps a cut off near the endgame. Games where defeated players have extreme power to determine the winner are obnoxious, particularly in games where you may need to hurt other players in order to get ahead.