Hey James,
If the Exchange server was already setup with SMTP Open Relay prior to the Amazon move, changing the IPs is all we should have tweaked after the move.
If not:
You'll have to set-up an SMTP open relay on your Exchange server in order for Method emails to go through. This is something I recommend you speak with your Exchange server Admins about, there's usually a structured way to do this - Microsoft Exchange, for instance, allows you to create "SMTP connectors" which Method can connect with (detailed here: http://support.microsoft.com/kb/265293). Method doesn't provide support for configuring Exchange servers. We recommend you contact Microsoft Exchange support for assistance in configuring your Exchange server to accept a Method SMTP connection (all they need is the list of IPs we use to relay).
Reason being every Exchange environments are unique and altering settings can cause issues in other areas, I recommend you run any changes by your Exchange Admins or Microsoft Exchange Support.
Let me know if there is more information you need from me and I'll be happy to assist.
- Mortaza