We can perform the migration with a real time sync. All you need to do is create Redis Labs DB(s) on the cloud to which you want to migrate, and we will do the real time sync behind the scenes. Once the DBs are synced, we will notify you so you can start using the new DB(s) with no service interruption. In many such cases our customers prepare a script that changes the endpoint(s) from the existing DB(s) to the new one(s) in all of the clients in an automated fashion.
Another migration option is to simply backup your current DB and restore it to your Redis Labs DB.