Using your theory, 31 episodes makes no sense. 13 would. 26 would. They had almost no clue what to do after the would tour, leading me to believe they had chosen a specific ending date ahead of time (and thus a start date for Double), and then wrote the story to fill out what they had left.
From the article/interview with Mr. Shadow said:......and we`ll have a special team up movie next Christmas too.
The future of Kamen Rider?
Well...MORE DEN-O of course.