I am guessing there is one more rule for Fury Bowser in the postgame: If all of your remaining Cat Shines are to retrieve the calico kittens, then the orange sky variant (where Fury Bowser remains until you collec a Cat Shine) cannot occur, as those are the Cat Shines that can only be obtained when Fury Bowser is slumbering.
Alternatively, you can collect a Giga Cat Bell and fight Bowser, then fight Bowser again on Plessie, but this would be stupidly time consuming and annoying.
Oh yes, and one more rule: When you begin the campaign itself, Fury Bowser's countdown will not start until you meet Bowser Jr. in the area between Fur Step Island and Scamper Shores.
Good to know I wasn't just being unlucky in seeing Fury Bowser almost immediately show up after one of the battles though, and that it actually happens every time...