Did some experimenting last night and found that the problem is with running Back and Restore from Windows 7 booted from my SSD.
When I boot from my old hard drive, I can run Backup and Restore from that drive, and when I drill down Windows Explorer to the SSD, I can run Backup and Restore from that drive as well. So, Backup and Restore has been fully migrated to the SSD and is fully functional.
It's only when I boot from the SSD that it doesn't work. In fact, if I boot from the SSD, and then drill through Windows Explorer to Backup and Restore on the old hard disk, Backup and Restore still won't work.
So, it works fine on the hard drive and the SSD when the OS is booted from the hard drive, but it won't work on either drive if I boot from the SSD.