5-1-4-a
5-1-1-e-2
6-3-3 (notice the rule says "has crossed" not "is across"...). Exception is "forced touching is no touching 6-3-4 and rules relating to a fair catch, 6-5-1-b.
6-3-6 This gives the kicking team legal possession of the ball based on above-mentioned rules.
I agree with the previous posts that "once across, always across" relative to scrimmage kicks crossing the neutral zone based on the rules above, and therefore the above rulings are correct.
However, to open another can of worms on a semi-related subject, the rulebook contradicts itself on relating to "once across, always across." See AR 6-3-13-III. Don't let this AR muddy the above rules/rulings. Those are correct.