I think you played it fine considering the stage of the tourney, your position and your read on the player. Best case scenario you had 17 outs if he had top pair or an over pair. AA, KK QQ, AJ, KJ, QJ. If you really thought you were behind I think 12-14 outs is the better calculation. A hand like JT, J9, J8, 9T, JJ, TT, 99, 88, 77 and you are still behind. All of those should be in his range. I disagree with you not wanting him to lay down a hand like KJ. Anytime you can get them to lay down the better hand at that moment is a good thing. Draws are not guaranteed. The only thing I strongly disagree with is thinking about check-jamming the turn. If you were going to make that move it is better made on the flop.
I would also consider check raising the flop but it depends on the read. If I think I am behind at the moment, probably not.
One thing I would have done differently is not shoved on the river. He was never going to call if he thought he was behind, and that was what you were broadcasting. Only a flush was going to call. I either check and give him one more chance to bet, then jam. Or just lead out a value bet on the river in the 4-5k range. If he has a real hand, straight, set, worse flush, he will be priced in to call, and it gives him the opportunity to make a mistake.
It was sort of fun breaking that down. I'm not sure if my analysis is right or not, but I've been away from the game for 4 years until about 3 weeks ago, so I'm knocking the rust off. It feels good.