CCC reporting physical problem with a drive volume even though the drive is working
In the end, I settled with Disk Utility. I know that CCC is typically faster since it copies in chunks but my goal was to create a one-time archive of an OS and then clone it to other drives whenever necessary so the benefit of CCC is less noticeable.

I found a forum post on Apple's forum about an issue that seemed similar or possibly the same. The accepted answer to that post suggested the older version of CCC was looking for mach_kernel files in the wrong place on the drive. Apparently, Yosemite and later now keep those files in a different location. Those particular kernel files are crucial to the boot process and the computer will not detect the clone partition as bootable unless those files are there. This explanation might explain my troubles since I'm using CCC 3.5.7 (unsupported) on Lion and the operating systems I was trying to image were High Sierra and El Capitan. Unfortunately, that forum post is lost in my browser history.

I never did try a new version of CCC because my early 2008 MacBook is incapable of running anything newer and I don't really have access to a newer Mac at the moment. I reverted to using disk utility which worked quite well. I created a read-only disk image and then, when I want to clone, mount the disk image and create a restore from the mounted image to the partition on the target hard disk.

Running Lion 10.7.5 on an early 2008 MacBook. CCC version 3.5.7.