$125 NL Tourney - Near the Bubble - Tough Call

[Any Two Suited]

My local casino's weekly $125 NL Tourney.
150 players. We are down to the final 3 tables. About 25 people. Top 20 pay.

I'm at about T10000. About average stack at my table, though below average overall.

For this hand, I am 3 off the button. Several lesser stacks between me and the BB, who is the chip leader, or close to it. Play has been tight recently, with raises taking down the blinds. The chip leader does not seem to be interested in playing sheriff.

Blinds are 700/1500. I have KTs, and it is folded to me.

I make it 4500 on the steal, which would put one remaining player all-in, and would damage some other folks between me and the BB (feel free to critique my steal attempt here, though that's not the gist of my post).

All fold to the BB (chip leader), who thinks for a few seconds, and then calls the 3500 more to him.

Flop: 3-9-Q rainbow, none of my suit.
BB thinks for a couple seconds, then pushes.

I've got about T5500 remaining, so I'm being offered about 2.75-1 here.

I try to think about what hands he'd just call me with, and then move in on this flop (I don't have him as the kind of player who'd make the "stop and go" play, so I gotta think this flop gave him something).

I rule out: AA, KK, QQ, as I think he would have just pushed on me on the flop.

Possibilities I come up with are: KQ, QJ, QT, JT, 99.

Against KQ and 99, I'm drawing to 4 outs, and don't have odds to call.
Agasint QJ, I've got 6 outs. No odds.
Against QT, I've got 7 outs. Just barely getting the odds.
Against JT, I'm ahead, with 8 outs against me, and 4 to a redraw for me if he hits an 8.

After thinking for a couple minutes, and hearing "PLAYER OUT" on another table - getting me even closer to the money - I decide not to gamble, and fold.

I did end up making the final 2 tables (finishing 16th overall). During the break, I approached my opponent, asking him what he had. He told me, and I'll reveal that after getting some thoughts on the play from you all.

Thanks.