Do you lose the maximum here?

I had this hand come up in an online tourney recently and I think there are a few different ways to play it but here is how I played it with my reasoning:

$24 buy in multi with 750 people, down to about 100 and getting close to the money. my stack: ~12k, villain ~8k. 200/400 blinds w/ante 50

villain min raises from cutoff, button and SB fold, and I have Jd5d and call the 400, getting ~4 to 1.
Reasoning: Although this is a bad hand, I think its way too tight to fold here to a min raise. I think he probably doesn't have too strong of a hand based on position and the min raise is probably a steal attempt. Since he is in this position, I expect a continuation bet after the flop and Im planning on a check raise all in if I flop any sort of pair or draw.

Flop: J-10d-9

I check, villain bets 1600, I go all in, he calls and shows KQ.
Reasoning: I stuck with my preflop plan, but Should I have? This is a flop that hits a ton of hands. Many hands will have me beat and a lot of hands that don't are still very live. It is possible he folds Ax,Kx or any weird 2 card hand that doesnt hit this, but there are a lot more hands that made a draw or a pair or both.

How do you play this hand? I could see some support for folding preflop, if you think the hand is unplayable. If played, Do you just call the flop since the board is so coordinated and hope for a blank or help? (the turn was the 8d by the way) If you just call the flop, how do you play the turn w/ 5k pot and 6k more in his stack? Also does anyone lead at the flop? are you calling or folding to an all in? Im pretty sure if he just calls on the flop, you are getting it in on the turn with the 8d coming.

I think there are a lot of ways to play this hand and I want to know which is the best.

really just depends on villian's image,

although im a complete tournament donkey, with 30BB, it seems if you want to defend your blind, 3betting him would have been an optimal play.

Idk if i like a 3bet preflop here... the problem for me is how much to raise and also the fact that we are giving away the great odds we were getting on a call.
I think if you 3bet, you have to make sure its enough so that he doesnt call and see a flop, but also so that you don't price yourself into calling if he shoves back. Making it 3k might be alright, but you will still be getting better than 2 to 1 against his shove. If you make it say 2-2.5k, I think you might be inviting him to call and then you are stuck w/ a bad hand in a big pot.
I don't think theres any way to make KQ fold at any time during this particular hand, except MAYBE to a preflop shove, but that is very risky and uncalled for at this point in the tourney.
The main question is still Is there anyway to successfully get away from this hand and feel confident that it was the right laydown?
I have thought more about it and I don't think theres any way out. However, if you did just check/call the flop and the turn was not the 8d, but something like a non-diamond 8,Q,K, or A you might feel ok check-folding here.
I think the way I played it is a bit risky but theres not much else you can do here.

The blind defense is fine, you are suited and getting 4 to 1.

I would lead out 600-1000 on the flop. The bet is for information, to make my decision easier for that street, and even the next. I think you get more information when you lead out with a moderate hand like this because if you face heavy resistance, you can come to more conclusions to fold (unless you have a read on the donk).

Plus when playing the J5s, I'm not looking to flop, and go broke, on top pair...........especially on a dangerous board that posseses redraws (unless you flopped top pair and a flush draw yourself, then you can make the argument to gambol based on your goals for the tournament). But with just a Jack and no kicker, on that board, even hands you beat that are in his range in LP like AQ/QT-Q9/T8-89, have plenty of outs to beat you, and I'd be more inclined to pitch just top pair and no redraw/kicker facing a big raise on that board with my tourney life on the line. With the bubble coming up, you can get good steal equity spots to get back the chips you lose in this hand as well.

Also make sure you take notes on the villain that he gheybet in late position and pot bet the nuts on the flop. It will definitely help your reads if you get in any hands down the road with him.

fold preflop.