Move file storage to another server
If all you're looking to do is offload your Files directory to a different server, and you have complete access to both servers, I would suggest you create an NFS (network drive) mapping to the storage server.

Then you can simply change your Public/Private files directory to /mynfs/drupal-files instead of /drupal/sites/default/files, which will pretty transparently offload storage to your other server.

You'll want to do some research into NFS and its alternatives that do the same thing.  I'm not familiar enough with the Storage API to know if it will work in your situation.  After researching it a little bit it seemed like you would have to do a decent amount of work as well.