Let me preface this by saying that I am not, nor will I ever claim to be, a great PvP player. I honestly consider myself to be a mediocre one (go ahead and look at older posts to confirm this if you don't believe me). I completed the majority (and when I say that I mean 90%+) of the Shaxx questline solo. Yes, there were times that I experienced the same things you discussed above, but I was still able to complete it. You just have to keep a level head, and keep plugging away. If you're at a part that doesn't require you to be in a Fireteam or specific playlist, head to Rumble. That way you won't have to deal with your teammates and you'll only need to rely on your own skill. It's not impossible, even for mediocre players.