Why does he need a "beef" with Kirk?
What drove Khan in TWOK was Montalban acting chops. All that nonsense you spouted was just something extrapolated from the off-screen ethos that Meyer threw in there to provide some evidence of a plot. Really, Khan of TWOK could have just have easily been "bland villain #230975." All the stuff that made him interesting as a villain and work as a formidable advisory was left back in "Space Seed."
The Khan of TWOK was neither physically superior nor intelligent. Those are ingredients that can work in any capacity, and if Bad Robot plans on using them, they may as well use ones that are familiar.