What I did, that worked, for my situation:
- Did the FS conversion, in place, as noted in the link in Randy N.'s post above
- Exited Disk utility
- Clicked on Install MacOs, in Recovery Mode, and let it reinstall Mojave. The Mojave install left everything in place (user accounts, applications, etc.). All this did was reinstall the OS and install the boot files; and, set up the disk to boot.
- Rebooted the system and everything was working fine.
- Then performed the update to Catalina.
My OS is on an external, USB attached SSD disk. The internal disk was available to boot, in Recovery Mode, to, in order to use Disk Utility. Because it is very difficult to replace an iMac disk, I went with the USB SSD disk. It is much faster than the stock 5400 RPM SATA drive.
This upgrade was performed on an IMac 21.5" mid 2015 system which has a maximum of 8GB memory. The SSD drive was a way to deliver high speed, without having to buy a new iMac, or having to pay to get an SSD installed. It turns out, for the Catalina update, it was good I had the internal disk to do this.
I have Time Machine running, and it was up to date, so I could recover if the OS reinstall wiped everything out.
It took under an hour to reinstall Mojave and upgrade to Catalina.
Everything seemed to work, as expected. I did not have any 32 bit apps, except Acrobat Reader, which I removed before I did the Catalina upgrade.
I hope people find this useful. Also, this may not work for everyone.