OK, thanks for the explanation. To confirm, from what you stated, it is the "old" clone, on your older HDD, that has issues. You already had a newer external HDD, and thus already had a bootable clone (via CCC, I assume) on it. But, for some reason, the "system" on that older external HDD had issues. Hence, that is where you want to replace "everything", correct?
Now, regarding El Capitan, OS 10.11.x. You mentioned you have been running OS 10.11.4. Did you originally download that from the App Store? Believe it or not, that is a critical distinction, as Apple has a bizarre philosophy regarding an attempt to retrieve either an older OS, or the one you want. Given that Sierra, OS 10.12.x, has been out for about 7 months, getting El Capitan could possibly be an issue. If you did download OS 10.11.4 from the App Store, then it still should be within your Purchases. Whether that is the case or not, what would be better is if you have the file entitled "Install MacOS El Capitan" saved somewhere on your backup/clone.. That should be OS 10.11.4. If you do have that file, or if you need to re-download it from the App Store (again, within your Purchases), it is actually easier to upgrade to OS 10.11.6 by downloading and applying thew OS 10.11.6 Combo Updater, available from here:
https://support.apple.com/kb/dl1885?locale=en_US
What I am unsure of is if you re-download El Capitan from the App Store (again, within your Purchases), what version it will be. If it is OS 10.11.6, then you would have the last version of El Capitan, and thus would not need the Combo Updater.
Regarding that "Install MacOS "whatever"" file, I always keep two copies of it, so that I do not have to re-download it. In fact, on both of my Macs, I have two copies of the file "Install macOS Sierra", and they are both for the latest version of Sierra, OS 10.12.4. There are times, for some "in between" Mac OS updates, where I just download and install (and of course save) the applicable Combo Updater file.
I certainly understand your wise decision about backups! I am actually somewhat more "paranoid" than you are! First, I use SuperDuper! for cloning/backing up both of my Macs to two separate external drives (actually SSDs). SuperDuper! is very similar to Carbon Copy Cloner, with two notable differences:
1. In US Dollars, SuperDuper! costs $27.95, whereas Carbon Copy Cloner costs $39.95.
2. Carbon Copy Cloner backs up the (hidden) Recovery HD partition, whereas SuperDuper! does not. That is not an issue for me, as 1) it can be re-created a couple of different ways, 2) if I want to run Disk Utility to "check/operate" on my internal SSD, I would first start up the respective Mac from the SuperDuper! backup, and run Disk Utility from there, 3) I have a much more robust disk cleanup/maintenance/repair program than Disk Utility, TechTool Pro, and 4) if I first Erase and re-Format the internal SSD, and then do a fresh, clean, "virgin" installation of the Mac OS, that hidden Recovery HD partition gets re-created anyway.
I do not use either of my machines in a "production" manner, and thus I only make SuperDuper! backups once a week. Like CCC, though, SuperDuper! can do scheduled backups. For me, it's just not necessary. About the only apps I frequently update are 1) Outlook for the EMials, and 2) Quicken for recording transactions.
In any event, the SuperDuper! backups are actually the third step in my weekly 3 step maintenance/backup processing. My routine is :
1. Every day, I am doing some disk cleanup (permanently getting rid of no longer needed EMails, removing no longer needed prior updates of apps, etc.).
2. For my weekly routine (typically on Saturdays), I first run the excellent freeware program entitled Onyx, for doing some additional (and useful) disk cleanup. That program also can Repair Permissions, something that Apple removed from Disk Utility ever since El Capitan came out.
3. Next, I run TechTool Pro, and I use a number if its useful features to do some more disk cleanup, disk maintenance, and when needed (which is extremely rare), disk repair.
4. I then finally run SuperDuper! and do my two backups for each of my Macs.
Doing all that results in my Macs being "lean, mean, and clean", and I rarely, if ever, have issues.
Finally, our oldest son lives in Richmond, and we were just there last month. In actuality, our time was "split up" in London: spent the first 4 days there, then the next 9 days in the Canary Islands (only Lanzerote), and then 5 days back in London. We had a good time, but I still prefer Seattle over London (and in fact to just about any of the other places we have visited, both in the US and abroad in Europe and Asia).
In any event, hope things work out good for you. Oh, and by the way, what are you using for a monitor (unless you replaced the one in the iMac)?