Jeremy Aurich has helped us!
Normal mail was flowing to customers and agents. Event emails were being stuck in the Spool. We checked EML files. We checked EHLOs. We checked Logs. Nothing seemed to point to a solution.
Basically, in version 11, when you go to Email in Settings, the default SMTP address is blank. We edited this to a) point to our exchange server and b) have a noreply@ address. Once we did this, we went into IIS and did a stop and then a start on our website. Restart doesn't seem to work. Once we did this, all event mail appeared to flow.
To SmarterTools - My suggestion is that the user be prompted to enter in valid SMTP data for the Default SMTP address. There should be a check for this upon upgrade from lower versions.