Hi James,
Sorry for the delay.
Based on your updates, I’d like to explain that the Office 365 accounts and the Microsoft accounts are provided by totally different services. While the integration via DirSync is just for the synchronization between Office 365 and the on-premises AD.
Currently, there aren't Microsoft articles describing how to integrate the On-premises accounts, Microsoft accounts and the Office 365 accounts. In addition, according to my experience, it's strongly suggested that customers not use the same custom domain in Office 365 and the Microsoft account (Otherwise, there might be multiple problems). I'm afraid that it's not feasible to achieve that.
Thanks,
David
