What you and I are doing is obviously an edge case and I am certain Apple has zero motivation to look into it. It just piqued my curiosity. I don't recommend it for any purpose beyond that.
In my case I had Bug Sur installed on an external USB 3 spinning HD. Booted from that with Startup Manager. Despite the fact it's a spinning HD, BS runs really well by the way.
I did not mount the internal Mac's startup disk. Did not even provide its FV password, so it's completely out of the picture. Then, I connected a separate, USB 2 hard disk drive with the latest Catalina release on it. Running Catalina compared to the USB 3 HDD it's rather a dog, but still completely acceptable for routine use after it starts up and everything is loaded.
Then, downloaded Big Sur and pointed to the Catalina disk for its upgrade destination. That began the arduous annoyingly long installation process you described. It may not have been the worst installation experience ever, but it's close. Multiple reboots and many useless progress indicators—as I wrote hearing occasional spinning hard disk noises helped, as was using Verbose Mode. At best it's a tie with Lion's first release.
But in the end everything worked, which is more than what I can say about Lion.
I have a screenshot that illustrates what I just described, but it's on an inaccessible volume right now. I'll post it later.