Everything is back online now.

For reference, the MSDN articles below explained pretty much everything you need to do. Worked awesome. Just another reminder of how crucial it is to have good backups of all your databases, especially the system ones. I can't even begin to imagine how catastrophic this would have been without good backups to restore from. Losing all our agent jobs, logins, replication, etc. . . (shudders)

The only other bit not covered below, is that the SQLServerAgent service would not start after following these procedures. Nothing in SQL error log, no SQLAGENT.OUT file, nothing in event log, it was bizarre.

On our system, the agent runs under a domain account. Not sure why, but some permissions were lost as a result of performing this procedure. After adding it back into the local groups below (local groups on the machine), all was well:

SQLServerMSSQLUser$YourMachineNameHere$MSSQLSERVER

SQLServerSQLAgentUser$YourMachineNameHere$MSSQLSERVER

Rebuild system databases procedure:

https://msdn.microsoft.com/en-us/library/dd207003(v=sql.105).aspx#Anchor_1

Restoring the Master database:

https://msdn.microsoft.com/en-us/library/ms190679.aspx

Restoring the model, msdb databases:

https://technet.microsoft.com/en-us/library/ms190749%28v=sql.105%29.aspx