ITM going for 1'st or 3'rd place with A7o - right play?

[Borax]

Did I do write to push here when I suspected two face cards? Or should I have just called or even folded? I thought that if my Ace held up here I would have a great shot for the first place....
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10+1$ SnG paying three places: 50-30-20
ITM with 3 players left
blinds at 320/640
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Read on player SB: had been showing me respect by folding everytime I played back at him
Read on player UTG: passive until ITM, still quite passive
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Stacks:
SB: 4210
BB (Hero): 3190
UTG: 2600
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SB: Posts small blind 320.00
Hero: Posts big blind 640.00
UTG: Folds
SB: Raises for 960.00 (small raise and I suspect KJ, QJ, JT, KT)
Hero: Went all-in 2550.00
SB: Calls for 1910.00
Hero
SB :Kc:
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Flop
:Jc:
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Turn

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River

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Showdown
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Hero
- One Pair
SB
- Three of a Kind
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Result
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SB Showed Cards (Winning) 6380.00
Hero Showed Cards left the tournament in 3'rd place winning 20$
UTG Mucked Cards
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[vqc]

if you put him on those cards, then you auto push this everytime. Get your chips in when u have the best hand.

Good push.

[ensign_lee]

at this point your stack is what, 4, maybe 5x the BB? Going all in here isn't a bad move.

[studboyjoe]

good play, he got a lucky hand and sucked you out. Don't change a thing.