Disaster Recovery Options for Sql Server
During Hurricane Sandy (natural disaster) and recently when moving our data center (managed failover), I was in your situation.

I have implemented Logshipping and was able to efficiently failover during the above scenarios.

The technique that I used was reverse logshipping (swapping roles between primary and secondary) - which allows you to swap the log backups. 

Below steps can be scripted with Powershell or TSQL script (I used sqlcmd and xp_cmdshell)

FAILOVER Process: 


Kill all user connections on primary server and take a final log backup (WITH NO RECOVERY) putting the primary  into NO RECOVERY state. 

a.This means that no users can now connect to the database and the database is ready for failover. 
Ship the transaction log to the secondary server  and restore the log WITH RECOVERY bringing the secondary  up. 

b.This means that the users can now connect to the secondary server as the database is successful failed-over.


FAILBACK Process: 


Kill all user connections on the primary server (original secondary) and take a final log backup (WITH NO RECOVERY) putting the primary (original primary) into NO RECOVERY state.
Ship the transaction log to the primary server (original secondary) and restore the log WITH RECOVERY bringing the primary (original primary) up. 


This will utilize less network bandwidth as it just has to ship small T-log backups.


  I do have a question about how log shipping handles Differential backups. Do I have to stop doing differentials for this to work?


A differential or FULL backup does not break LSN chain. ONLY an adhoc log backup will break the LSN chain.