I apologize if that's the tone I'm relaying. I guess I'm just frustrated due to the time it's taking to fix it.
Since it sounds like you guys are talking about straight up file storage I'd guess a good option would be to set up an HDFS cluster and be smart about locality/replication to minimize the latency.
Edit: Oh, and one more thing is take a backup that doesn't involve EBS snapshots. Maybe biweekly dump the entire sucker to S3 or something or have it getting pushed there all the time. This is something we've been meaning to do since the snapshotting capabilities of EBS are still a bit too magical for me to sleep well at night. (To be fair though, they've worked great when we've needed them to.)