The reboot was just performed successfully, about 8 minutes of total downtime. This was performed under advisement by HostGator to lift some network limitations they had in place which were causing issues with the new backup solution.
And before anyone asks why... I honestly don't know why for certain, but if I was to guess it might be because HG have Dave's server running as a VPS on a dedicated server (ie, dedicated only to Dave) and the restrictions may have been on the VPS instance itself.
Edit: Confirmed, we are now seeing excellent throughput to the backup system.