Calling all-in with AK late in MTT with healthy stack

[vandyhawk]

Here's the situation. We're down to 14 out of about 345 in the Bodog 3.5k guarantee ($10 entry). I had been crippled but managed to double up a couple times in the last orbit to get to 34k, which was right at average. Blinds were 800/1600/150 for opening pot of 3450, so my M is about 10. Here are the stacks:

UTG: 88k
UTG+1: 20k
MP: 59k
CO: 37k
me: 34k, holding AsKh
SB: 67k
BB: 13k

The other table had far fewer chips total than mine, and I think I was in 7th overall at this point. First three players all fold, and player in cutoff pushes all-in for >20x the BB. I hadn't been at a table with this guy all tournament until we hit the final two, which hadn't been that long ago, so I didn't have much of a read on him. My gut and poker sense told me that he wouldn't be doing this with a very strong hand, as it's quite the over-raise and he's not desperate. I initially put him on a mediocre ace or possibly a middle/low pair that he doesn't want to fold but doesn't want to face a tough decision with if he gets called or re-raised. Of course he could have trash or AA/KK too, but unlikely. Here are the pros and cons I came up with at the time for calling.

Pros:
I'm likely far ahead or am at worst a coin flip.
If I win, I'm second in chips with a monster stack and ready to make a solid run to the top three where the real money is.
I've been on a rush (not really important but could be influence at the time).

Cons:
It's not a made hand, and there's a chance we're racing.
He could be pulling an elaborate push to make ppl think he's weak when he really has AA or KK ploy (unlikely though).
If I fold I still have a healthy, average stack.
I lose and I'm out.

What is your play here? What range of hands do you put him on to help you decide?