Android Outlook IMAP: Microsoft account interference in configuration

The problem here turned out to be the specific email address involved (autodetect was working as well as it could given some absent DNS entries; and anyway, as I now realise, autodetect/autodiscover means something different to every email client, and autodiscover specifically is really just an Exchange thing anyway).

I got suspicious once I had tried another email address in the same domain and it worked perfectly.

I had an old Hotmail account set up on the 'phone and tablet for various things (Windows Phone Companion, OneDrive, etc.) This Microsoft account had at one stage included an alias of the offending email address. I had got rid of this alias right at the beginning of this episode, but clearly the 'phone still thought it was there, and in particular Android Outlook was confused by it. Once I had tried on a brand new Android instance (via BlueStacks) and it had worked perfectly, I realised the situation, removed the Hotmail account from the 'phone, and Eureka.