I suppose a couple of things. First, the backup image needs to be on the Root directory of the external drive. It can go on another directory if you are using a Network Location, but not usually a external drive.
Secondly, a new drive would be clean and not have a prior OS for the system to see. If it thinks you want to re-image Windows 7, that is what it looks for. You might try using Diskpart to clean the drive before you try to re-image back to Windows 10. Don't do this if you current drive contains the recovery for Windows 7.....
I haven't tried a repair disk, but you can download an .iso of the preview builds and use it install of the Repair Disk.. it may not be faster, however..