So for the record, it was a problem on our end, not Sony's end, and I think it was 100% unrelated to the network blip.
Turns out we had a DNS cache that timed out and failed to refresh correctly, which prevented the login server for each cluster from talking to SOE's authentication servers, because they couldn't resolve the auth server names to IP addresses.
I think I'll put measures in place tonight before I go to bed to make sure this doesn't happen again.