You could start with making it impossible to join a game after the first half is over. To me, it is the single most important thing you need to fix. Now, I just leave and search again if I come to a match that is too far gone. So this problem generates other problems, and it has been like this since I started playing (launch). I hope you adress this very soon and that you share the opinion that it is a very urgent matter. In fact, if not fixed - nothing else matters!
Matchmaking should be prio 1