PokerStars $500k - Help Please

Yesterday, I was involved in a hand late in this tourney that I wish I could play over. Around 3200 entrants with 200 left, and I'm sitting in 38th with 52k. Average is 28k. I get AKo, and the blinds are 3k. Almost all pots are being taken down with a small raise.
An EP player (w/54k) makes it 8k, and I push in LP. He thinks for almost the entire two minutes, and calls. He turns up JJ. I'm out in 200, and he's 2nd. I've been thinking about this hand, and decided that the following were my choices:

1) Make a small raise of 2k more to see where he's at. (this would be for about 20% of my chips) If he reraises, or pushes, then I fold.

2) Flat call to see if I get any of the flop (prob. my best option), and puts me around 44k or 80th.

3) All-in (my option), and hope that he folds, or has AQ/KQ/AJ or AK even.

4) Fold

I think I made a bad play here. He gave me a chance to see the flop, and not take a huge loss. I could've worked my way back up. I don't even consider folding here. I'm in this to win, or at least final table. I'm already in the money, and 200th to 30th is not that much different. I would've been 2nd had I won this flip.
He went out a few hands later with QQ vs AK vs A7, and the turn is an A. Almost all the remaining players were pushing in with AK. I wonder if you have to resign yourself to getting in this type of coin flip to generate the huge stack it takes to win?
I would like some input to see what everyone else thinks.

Thanks in advance!