Thanks for your insights/comments, MacManiac. For Onyx, it looks like Titanium Software "recently" went to specific versions of Onyx for specific versions of the Mac OS:

http://www.titanium.free.fr/onyx.html

I have no idea what would happen if I, for example, downloaded V 3.0.1 of Onyx, and tried to use it, given that I am now running El Capitan. I don't want to try!

Also, I took a previous item you pointed out to test. I just completed my weekly maintenance tasks, and I just re-booted my MacBook Air from the just completed SuperDuper! backup (was the second one). Although somewhat slow, it did eventually complete booting successfully from that just made backup/clone. So, at least one of them is fine. (I'll try the one for my MacMini soon, as I am entering this post on it).

I still want to look at purchasing a Samsung 512 gig SSD (not sure if it will be an 850 EVO model, or an 850 Pro model) to place in an external case for my backups. Once again, though, I still need to find such a case with a Firewire 800 connector. I'm assuming such a combination, instead of my present hardware for that (a Firewire 800 connection, but a 7200 rpm Seagate HDD), would be faster.

The booting of the Mini from the most recent SuperDuper! backup also worked, although once agin, it was somewhat slow. (Edited for that additional comment)

Last edited by honestone; 02/27/16 10:51 PM.