You're overlooking the obvious. Nothing in TWOK would have affected Chekov's career. Khan's escape was unfortunate but could have happened to anyone who visited Ceti Alpha V. The likely reason for Chekov's inability to gain a command of his own is due to his participation in Kirk's hijack of the Enterprise in TSFS. The formal charges against the former Enterprise crew were dropped in TVH (except Kirk's insubordination charge), but that doesn't preclude Starfleet holding off on any promotions for the foreseeable future.
Now you're overlooking the obvious. Why single Chekov out and punish him for participating in the hijack of the Enterprise? Sulu made Captain, Kirk got a new ship for his demotion (reward), even Scotty made Captain (of Engineering, whatever that is) but poor old Pavel is held back? Sorry, that doesn't make sense.