I would have put the brakes on when I saw the K at the flop.

Fold to any significant raises.

If they check to you, bet for information (like .70) but nothing like
what you did.

Then I would have watched for strength. When they see you
bet they will immediately put you on a Kx and will call or raise
if they can beat it.

If they raise, you fold.

If they call start checking and only bet if you can be sure they
don't have the K.

In this case I would have folded when they went AI. But I would
have saved alot of money.