Just wanted to post an update in case some future reader encounters a similar problem. Bottom line: all is well.
I did need to go to Plan C or D to make it happen, though.
For some reason, while the drive was cloned successfully (Plan A) and showed up during a Restart-Option (to choose the external drive as the startup), the rotating gear would never stop. Argh. Sure it's a slower external USB drive, but bootable. Did not happen.
Plan B: boot into the Recovery partition of 10.8.x and reinstall from the Time Machine backup onto the external drive. The process started and got to 12% complete when a "Can't Continue, Restart" error message popped up. Arghh. So something on the Time Machine backup is corrupt (it does include System files)? Disk Utility verification said the structure, etc. are all OK.
Plan C: so maybe the Time Machine backup, which does include a System, backed up something from the original HD that was physically corrupted by the failing internal disk. So, boot into the Recovery partition and do a fresh install of 10.8.x. This happens as an Internet connection download and took hours, but was successful. Now OS X thinks the drive is a "new computer" and offered to set it up in a variety of different ways. I chose Migration Assistant (not Time Machine), which would bring over only user files, applications and settings. Success!! Running off of the external hard drive.
Did some App Store updates, one of which required a restart. Did the Restart-Option thing and external drive did NOT appear. Arghhh.
Plan D: The restart finished off of the old internal HD, went into Preferences>Startup Disk and the external was listed. Chose it, restarted and all is well again.
I'm not sure why the external USB drive appears in one startup place and not another, but it might be the USB ports? The external is directly connected, not through a hub, so any observations would be appreciated.
