Mac – Time machine backups getting corrupted

It is my understanding now that all Time Machine backups after the initial one are a diff of the previous backup, not a disk image. So deleting these folders would render subsequent backups useless (I think).

Fortunately that is not the case. Time Machine backups are complete backups, but they share the disk space with previous backups for the files that have not changed (using hard links). As long as any of the hard links is available, you can access the file.

So if you have a big file in Monday's backup, and the file has not changed on Tuesday, the same file will exist in Tuesday's backup as well, but it will not take up any extra disk space. You can safely delete Monday's backup, and the "copy" for Tuesday will continue to work.

The "Preparing to empty the Trash ... Items to delete: [number]" dialogue got up to 1.5 million files(!) before I stopped it. And I don't have permission, even as root, to rm -rf them.

Yes, because of these hard links, there is an insane number of files in a Time Machine backup (they are all counted so many times). You cannot use simple file-based tools on a Time Machine backup, you need something that understands (and preserves) the hard links. For example, if you tried to copy all the files on a Time Machine disk you would end up with huge duplication. The only way to copy/backup a Time Machine is cloning the disk structure (using something like Disk Utility).

Try this:

sudo tmutil delete /Volumes/yourTimeMachineVolume/yourTimeMachineFolder