Solution 1:

According to Microsoft, you can sysprep a Windows 2012 server running RDS. Since you already have a backup of a functioning server, you can:

  1. Restore that backup.
  2. Disconnect the network cable.
  3. Boot the server.
  4. Make sure you have a functional local administrator account.
  5. Run c:\windows\system32\sysprep.exe and pick OOBE. You don't need Generalize unless the hardware is different.
  6. Reboot.
  7. Let the server boot up to the login screen.
  8. Connect the network cable.
  9. Log in as a local administrator.
  10. Join the computer to the domain.
  11. Proceed. (Profit?)

Solution 2:

Your best bet is to build a new server, join it to your domain, then configure RDS on it. Imaging an existing server, and then attempting to break it down and reform it into a new one is going to be a huge headache.