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I'm not sure but maybe the TM disk has a /.fseventsd folder, too? I don't know if TM is using the fseventsd on the backup disk as well, if yes then maybe the fseventsd database on the backup disk was corrupted?
I guess it would help to put "The server encountered an error processing registration. Please try again later." in the title. It's a more or less "popular" string in the Google search field :-).
I'm glad this worked for you and I agree a deeper understanding would be nice when you search for 'The server encountered an error processing registration. Please try again later.' you can see that we are no alone with this problem :-).
You can add as #11 :-) to remove /Library/Preferences/com.apple.applepushserviced.plist (dont forget the reboot :-)) it contains some unique Machine identifiers…
Check imfreedom.org/wiki/IMessage for informations about how iMessage works and maybe you can use the tools I mentioned above to monitor the programs. It looks like that 'applepushserviced' is responsible for the connection, you can turn on debug logs for this program (how you do this is described in the link). I saw that 'applepushserviced' has a keychain '/Library/Keychains/applepushserviced.keychain' you can check if this keychain is maybe corrupted on your system.
Another idea is to check if something blocks the ports of the 'imagent', do you use programs (IP-Filter) like 'Hands Off!' or 'Little Snitch'? An IP-filter maybe blocks the outgoing connection. And turn of the Mac OS X 'Firewall", just to make sure that nothing blocks the ports of the 'imagent'.
