Decided to try a CHAT 24x7 tonight and after 1 hour I got my solution.
My incoming mail server is set to IMAP-mail.outlook.com which is fine - no change there.
However, my outgoing SMTP server was SMTP-mail.outlook.com as recommended in the guides.
We changed this to mail.bigpond.com and immediately my problem was fixed.
I gather there are less stringent spam checks on this SMTP server???...
Hopefully itthat server stays active so my email keeps working...
I can now send emails to people and they see only my alias mydomain.com and not the bigpond address.
Excellent!!!