I can reconcile that. The clock is related to the down; not the play type. And the kick down trumps the other factors (as would a score).
More worms? Rule 2, Section 7 defines two types of downs with an additional "exception" for a try down. They are a
scrimmage down and a
free kick down. A scrimmage kick play, pass play, running play, etc are all potential play segments within a single scrimmage down and are defined in Rule 2, Section 30. The directly conflicting definitions of plays being discussed here IMHO overlaps into the down term as defined and used in other places in the rules.
Maybe part of the solution here is to add definition(s) to Rule 2, Section 7 defining exactly what a "legal" scrimmage kick down is and any other down definitions needed (maybe passing down?). Or maybe revise the existing definitions of plays in Rule 2, Section 30 to make them mutually exclusive? Or maybe some combination of both? Or maybe get creative and simplify the two sections by combining them into one section that defines downs and the plays that can happen within a down?