Hi Kleinandsheridan,
I notice that you said "you can see that emails to the accounts are bouncing around something called a 'forefront' server like a pinball before finally being rejected".
Forefront Online Protection for Exchange (FOPE) is a hosted service that incorporates multiple filters to actively help protect businesses' inbound and outbound e-mail from spam, viruses, phishing scams, and e-mail policy violations. FOPE helps minimize capital investments, free up IT resources to focus on value-producing initiatives, and mitigate messaging risks before they reach the corporate network
What plan of Office 365 you are using now?
If you are an E plan user, you can configure the FOPE settings in Office 365 for E plan, you can login to Office 365 MOP page, click Manage below Exchange, then click Mail Control, you will see Forefront Online Protection for Exchange, click Configure IP safelisting, perimeter message tracing, and e-mail policies.
For more information:
http://technet.microsoft.com/en-us/library/ff715282.aspx
Thanks,
Bourne Zhang
