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I think we can put villain on a hand here that will either fold to any form of further aggression or a hand that crushes me.

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If this was 100% true then you are right that it would be either a b/f or c/c down and c/r would obviously be an incorrect play. If it hypothetically was true, then I am sure that c/c down would defenitely be the greater play because a b/f would too often make you fold to a bluff or a split and miss a lot of value from the bluffs he will make if you c/c compared to the times when you save some money when behind. You are just not behind often enough for b/f to be the better play imo.

But I really don't think it is that black and white here.

Someone else suggested a small bet and a $50-70 bet has to at least be an alternative imo. It would look really weak and sometimes induce a bluffraise. It could also sometimes trap him, making him call both streets with 2nd pair. Most of the time it would fail, but the times you stack him are worth a lot. Against a more LAG player I think thats the superior line.

Against this villain however I think check/call turn and probably shoving river is best, and if he checks through the turn I vote for a bigger bet than just a half pot. Make it closer to 2/3.

I just think that he will put in more money more often if you take an unorthodox line that doesn't represent a King as strongly as c/push would.