Disk Utility has been running for 3 days on task "checking multi-linked files" on my Time Machine backup disk

I would be suspicious of the time machine disk.

I would get another new external disk, connect it, and add it as a Time Machine disk. It's always safer to have two backups rather than one. I would also reboot the computer and run Disk Utility on the computer's main disk. Assuming it is healthy, I would suspect a problem with your old Time Machine disk. You could try to erase and reformat it but it will always be suspect, best to simply replace and discard it, you will never be able to really trust it.