Yes, seems like you've thought this through thoroughly. Every DO secondary will ask "why DO, why osteopathic, why us?" or some variation of that. In your secondary, you can hit the reasons for your interest in DO specifically.
Even though the DO essay is longer, I'd be carefully about getting to wordy and lengthy (Adcoms have to read thousands). If the shorter version suffices for AMCAS, it's def fine for AACOMAS. Again, I'd keep it to the story of why medicine and your path to get here - why am I certain medicine is my future and why I am the perfect candidate.
You could hit DO briefly if you'd like, but you'll have multiple essays later for that.
Good luck!