No news from service yet. Sorry
Woke up and realized my level of trust in the email service was very low on the points at issue.
I did not want them coming back and saying that it would have worked if emails had originated from some other domain, and so I copied your test environment to the other two domain; ensured permissions were OK; and tested satisfactorily.
Makes me feel better to inform them that they can now use any of the three domains to send to any FROM address for 9 variants. All provide same default address, as they can observe for themselves.
Will be in touch when they respond.