Time Machine Backups Gets Stuck With 100% CPU via tmutil
I had a feeling I might have posted this too soon; just had Time Machine's normal backup do the same thing.

However, the culprit I discovered was that somehow I had a .inprogress backup that was older than the most recent backup (in fact there'd been five or six successful backups since). No idea how it got there, but sudo tmutil delete &lt;path to .inprogress file&gt; solved the problem.

I'm not sure if I'll mark this as the correct answer or not, as I still have no idea how I ended up with a leftover .inprogress file, or why it only started causing problems when it did, or why it didn't always affect automatic backups…