I'm surprised that no one replied to this. But I learned a few things that may be helpful to some of you with this same question.
When you restore data from an external disk drive with Time Machine files on it. As you move through the dialog (in either System Startup or in the Migration Assistant) it will ask if you want to restore from an external disk with Time Machine files. If you select this option, it will show you only one Icon. You will expect to see your external disk drive listed as the source of the restore. The icon that is shown will look like your ilnternal drive and will be labeled something like Macintosh HD. That is not your internal drive, but is your backup drive. It is labeled the same as your internal disk drive and it is telling you that you have found the backup for your internal disk drive.
Would be nice if Apple would put a note of explanation about this as part of that dialog. I wasted several hours trying to make it work Finally I took a chance and selected the drive shown and it did restore my system. I ended up with two users since I did it from Migration Assistant. Had I done it from the System Startup, there would only be the one user.