I was thinking in general terms. I think an "average" player is suspicious when you check a K high flop in position after reraising preflop. This is obviously player-dependent, but I think a random player cannot be expected to make weird bluffs or really loose calls as a result of a flop check here. Of course it is possible, I simply don't think it's probable.

As far as balancing lines is concerned, I thought about that as well. If I'm going to bet here after reraising preflop with A-J, I'm not going to check when I pair my king on the same flop.

Frankly, I think you're overthinking this situation a bit. Just bet and expect to take down the pot.