Hi ThomasBrown,
Thanks for your update.
Based on the error message that you have provided, the issue caused by the reason that you don’t use the third-party SSL certificate, therefore, Outlook cannot connect to Office 365 via Sigle Sign-on (SSO). To resolve the issue, you need to use a third-party SSL certificate when you configure SSO. For more detailed information, please refer to the link below:
Configure single sign-on: http://technet.microsoft.com/en-us/library/hh967628.aspx
Best Regards,
Anna Shi