Sounds like the tube may have been out of alingment from the start, and when it got hot, it moved some more.
The one thing that I will do on a new key is to clean up the opening to remove any burs (use slightly greater angle counter sink) and the opening shape edge (if you do get deflection, it's less likely to do some damage to the tube). Then pull the hand guards (allows you to bend the tube to the correct location/center) and test the tube to key on a very slow lock. If needed, I will slightly bend the stock tube to make sure that it is feeding dead center in the key. It helps to pull the bolt to be able to see the tube enter the key, and feed the carrier with my finger to see the relationship of the two, due to slop/movement of the carrier in the upper.
Best bet is to order a new gas tube for when the old one takes a dive or just replace the damaged one. Since the gas tube is fairly cheap, and I haven't seen the amount of damage to your tube, you may want to just replace the tube since fishing the broken end out of the key could be a real bitch and turn the rifle into a single shot at a less that ideal time.
Hope this helps in some way,
Dano