Hi Happy;
Thanks for the info but I came across a YouTube video that showed how to convert your internal HD to APFS even with files on the HD. Other sites had the same procedure but the video had one difference. In Disk Utility and in Recovery mode, you go to the View menu and check off Show all Devices. Then you highlight the Macintosh HD in the Disk Utility sidebar, then in the Edit menu you find Unmount and click on that. After that, go to the Edit menu and the Convert to APFS is now highlighted.
So far so good. I clicked it and Disk Utility converted the HD to APFS no problem. Just when I thought all was well, I rebooted the HD and then it went right back to the Recovery mode and I didn't press any keyboard buttons. I kept trying to reboot and the same thing kept happening. I went to select the HD under the startup command and I got an error message. It was not looking good!
So, I took my bootable backup drive to get into the iMac again and then I brought up Carbon Copy Cloner to restore the HD from the backup, just to see what would happen. It didn't take long as I did not erase the internal HD and it just replaced some files. It was late, so I left it and didn't bother to reboot the machine off its internal HD after the restore was done, as it was getting late.
I didn't think it would work but when I booted it up this morning, it worked! I got in fine and the internal HD is now in the APFS format with all my files! I don't know what happened during the restore but it fixed the problem, and without having to erase my internal HD. The bootable hard disk is still in HFS+ and I'll leave it that way for now.
Next step is to upgrade to Catalina but after all the stress from last night, I'm going to put that off for a few weeks until I get up the nerve again to try. At least the iMac is APFS converted and that's fine for now!
Thanks for your willingness to help. Much appreciated.
Cheers,
Ed