You both had big hands, both preflop and on the flop. You were
about even when the chips went in. There wasn't a reasonable way for you to avoid losing all of your chips.
Preflop, I think you should raise. ATs isn't so great if you are in early position and there are 8 players who might find QQ after you. However, in blind versus blind situations, AT is a very strong hand. You can raise with a lot worse, particularly if there are antes, and against an opponent who knows to raise with a lot of hands, you can reraise with AT or call all-in.
People greatly overvalue survival. Folding all except monster hands in the hope to make the money or climb a place or two is a common, exploitable weakness. The value of survival mainly tells you to be cautious calling all-in, and it normally only raises your calling threshold by a few percent. You pushed rather than calling all-in here, so the value of survival has little effect here.
On the flop, you have a very strong hand, and should expect to be ahead the vast majority of the time, particularly since your opponent did not raise preflop. I think you should bet out to avoid giving someone a free card with a gutshot or a flush draw or bottom pair. If you think he will bet with nothing, though, check-raising will probably get more money in.
With a pair plus a flush draw, there is no way he was going anywhere, particularly because he can expect to be ahead much of the time. A pair+flush draw has 9 outs to improve to a flush, and 5 more to improve to trips or two pair beating top pair.
Your check-raise on the flop was slightly out of proportion to the size of the pot. If you called the bet of 800, the pot would be 2400, so your raise of abotu 5000 more chips was twice the size of the pot, giving your opponent about 3:2 odds. As an alternative, you could consider raising to about 2400, then putting the last 3500 in later, but raising all-in was not very dangerous. Raising all-in for 5 times the size of the pot would be much more dangerous; you would get paid off by fewer weaker hands while you still lose your stack most of the time against better hands.