I went to the most-recent clone (Backup A). It wouldn't boot -- same error. As before, you can still read the drive as an external hard drive, and I therefore recovered such files that had changed (I think) in the one day since the previous clone.
I went to the older clone (Backup B), this time first putting it in the other laptop: it booted without a problem. Before proceding further, I left that drive in place and cloned it over Backup A. I then put A back into the main computer and it booted. Before I left for my dentist appointment this morning, I set the computer to clone newly-recovered Backup A into the Primary drive.
I really wish the balky computer would fail a diagnostic test so I would have a better case when I call Dell tech support. OTOH, Dell may not give me the time of day, either; although when I look up my system's extended warranty status, it says I have over 200 days remaining, when I tried to actually initiate a service call, their system responded, "Your service contract has expired." I will have to telephone them and argue with them over the phone, assuming I can even get that far.
This state of affairs is intolerable. I'm planning on swapping a working clone (of the prime/A/B set) into the other computer and using the other computer as my main machine for a while. If the problem really is hardware related -- faulty motherboard/controller -- then the backup computer shouldn't have such difficulties.
Meanwhile, I think I'm also going to see about going through my files and flat-out archviving -- as opposed to backing up -- a good chunk of My Documents. Having these constant scrapes with disaster is not good for my peace of mind.