'Stars $11R; My friend thinks this was a bad move

[Superfluous Man]

Scenario: About 170 left in the 'Stars 20k guaranteed rebuy last night. I'm sitting on a stack of 16600 after some dude hits his 4-outer on me to take half my stack. Big blind is 1200, antes are 50. Average stack is in the neighborhood of 27000.

Hand: UTG+1 (stack size about T22000) makes the typical raise to 3600. My read on him is that he is typical: tight, decently aggressive. I put him on QQ-77, AK-AT, or KQs (I suspect he would have tried a limp-reraise with AA-KK). I'm in MP with AKs. I think for a little bit and push. My friend, who was watching, thought I was insane. I thought this was a no-brainer push. Please tell me I'm right.

My rationale:
1) There's almost T6000 worth of dead money in the pot if UTG+1 folds to my reraise. That's increasing my stack by almost half if he gives up right there. Of course, if I raise at all, it has to be all-in.
2) Calling sucks, as I don't want to give up almost a quarter of my stack, then have to fold when the flop whiffs and UTG+1 bets out.
3) Folding is bad, because I'm playing to make the final table, not to sneak into the money. The blinds are going to hit me soon, and if I double up now I'm right near the average stack, in good position to make moves. Just like before the rebuy period was up, I felt it was time to gambool or go home.

Thanks, I look forward to you guys telling my friend he's weak-tight.

Edit: Forgot UTG+1's stack.