The main problem is in question actually. I've already posted a couple of times that your aim in MTTs mustn't be to hit ITM. What you get, a possible double buyin? Anyways, if you find yourself in situation like that, you should play exactly how you did in this specific situation, ofc push with pocket sixes if you are under 10bb. You were unlucky tho, but around 50% for you to win the most important hand just isn't enough...bubble phase is where YOU take adventage over small stack, push them harder and you might finish at the FT more often.