OS Reinstall errors in Recovery Mode on 2012 iMac

My Late 2012 iMac running Catalina (the most recent OS supported) stopped booting up this week. It would just give me the circle with a line / grey error screen. I could get into safe mode but that would soon crash too, and was too laggy to even run any diagnostics.

In Internet Recovery Mode I could run Disk Utility which identified errors in both Fusion drives (SSD and HDD) in red text, and suggested "fixing" them to working order, which I gathered would wipe them. I didn't want to lose everything but I couldn't access my backups, as the external drive suddenly needed a password which I never set up (or forget setting up). So, the options remaining were to try an OSS reinstall or go ahead with the drive "fix" aka formatting on the iMac's hard drives.

OS reinstall was to Mountain Lion, as that's what this late 2012 iMac shipped with, but that wouldn't work. No drive icon would appear and the OS install couldn't proceed. At a loss, I gave up and went back to disk util to try too fix my broken drives. That ran through quickly, but since "fixing" my drives, the iMac won't boot in regular OR safe mode, and just cycles through crash > "your mac restarted due to an issue" > flashes code on the screen then reboots. Rinse and repeat.

The only mode I can boot up is Internet recovery. After having done the drive reformatting, I was able to proceed with the Mountain Lion reinstall. This gave me some hope. However at this point I've tried five times, and each time after downloading the OS I get an "installation error, try again" message.

Trying again does not work. I have no idea what the issue is, as the Internet connection is fine and the download occurs, it just won't install. Maybe Mountain Lion is too old, but it doesn't have an option to change what I install, in recovery mode.

My other options include trying to create a USB boot disk for Catalina, from my working MacBook, then try to get the iMac working off it. But not sure it's worth the effort.

I realize many would just give up and move on in this situation with such a "legacy" iMac, but it's sad as it was just working fine until this week. I love the screen space and I did have a lot of important stuff (mostly personal photos etc.) on those drives, which I've likely now lost anyway.