JPO4 - final hand

A week ago I played in a local radio show's poker tournament. It was held at the Borgata. The field was pretty tight - at least at the single table I played at. Most things were uneventful - until the final hand, which I'm still thinking about.

Blinds are 300/600 with a 75 ante

I have 14,000 in the BB.

UTG + 1 (a good player) raises to 1600. It folds to me. I call with AKs (spades).

Normally I might raise here being out of position, but a raise would have been to 5000 or so, which would have been 1/3 of my stack, and I wanted to see a flop before committing so much so relatively early in the tournament. It was the 6th level.

Flop comes 987 (two spades).

I bet out 5000 (pot is 4250). The other player who started with 16,000 stares me down for about 40 seconds and then pushes all in. I insta-call with two overs and the nut draw. He flips over TT and two blanks come on the turn and river.

So was my call correct? Should I have pushed after the flop with 4250 in the pot? Check raised the flop?

Well - let's just analyze the decision I was faced with . . .

There is 16,650 in the pot when he puts me all in. And I have 7400 left. I'm getting 2.25 to 1 pot odds. I had at least 9 outs with my flush draw. Those had to be good. Then of course with the extra 6 outs with two overs, I had 15 outs. So the call was correct. PokerStove says I had a 50.8% chance of winning the pot.

But what I'm trying to do is win pots without showdowns. What could I have done in this hand to not see a showdown? Be the last one to put in a raise. Oh well.