Hand question to get feet wet

First post, so just tossing in a recent hand for suggestions.

Final table, 3 players. Blinds 200/400. I've got about 3000T, and the others have 8000 (the one to my left has a bit more, ~8500).

I get AT of diamonds (best I've seen in some time). Leader raised UTG to 800, SB folds, I raise to ~1200 he re-raises to something less than me being allin. I reraise allin and his AKo holds up.

The question is, given his rr preflop is my only chance to call, and then push allin after flop? is there any possible chance of him folding then (pot would be over 4000 and my remaining stack was something like 1500) or does it merely change the order of the action and AT v AK is going to get allin in this situation? Did I make a mistake earlier by re-raising? Would just calling his raise, and then leading with a bet to a smaller pot (the flop missed us both) have a better chance?
At the time I figured him for a standard raise with any hand and that any raise would make him fold. But then afterward, I wondered if I could've played it differently. Would like opinions.
-q

[Lloyd]

Your mini-raise is not good. 3-handed you have to think that you're AT is the best hand. With your stack size (less than 10 BBs) you're either all-in pre-flop or folding. So when he raises you HAVE to push. There is absolutely no other reasonable play in this hand. Even if you just call and push a flop that he misses, he'll probably call because of the odds. That's why you need to just re-raise all-in pre-flop and hope that he has Ax.

[illegit]

You could just call preflop and then push any flop (i.e. stop n go). in this spot I think it will often gain you some fold equity. Your hand is fairly strong for 3-handed so if you want to push preflop that's fine too. I'd probably try a stop n go here.

[Lloyd]

The main reason why I wouldn't want a stop and go is that I'd like to bring Ax along pre-flop and not fold to my push on the flop when he misses.

[TomHimself]

yeah you lose value with a stop n go against hands you beat that might call pf but fold on flop

[illegit]

[ QUOTE ]
yeah you lose value with a stop n go against hands you beat that might call pf but fold on flop

[/ QUOTE ]
Right..but you gain value when hands that beat yours and fold. A2-A9 and KT are the only hands that you really don't want to fold out (you're ahead of KQ, KJ PF but they'd be getting proper odds to call a push thus that's bad given the fundamental theorem). Considering the size of the pot already I'd rather risk folding some hands I dominate if it also folds some hands that beat me (or could with more cards) seeing as I can increase my stack by 50% without even having to show down, or see all 5 cards.

ATs does have definite show down value handed so a push is fine too, but i think a SNG is probably slightly better.