(Not having reps from each chapter in the council seems so foreign to me!)
Just curious - though you are not on the board, can you propose motions to amend bylaws (assuming you could find the bylaws)?
You really need to talk to the Greek advisor and get a copy of these bylaws; being expected to abide by bylaws you don't even know is ridiculous. If he / she will not listen to you, go in a group. Get your brothers behind you on this.