Ugh. This works, but it's ugly. There are a lot of automated tarsnap assistants on github; I made one myself.[1] They can do helpful things like allow for daily, weekly, and monthly backups, keeping a certain number of each. (And personally I like giving each folder its own archive, and I dislike having slashes in the archive names.)
[1] https://github.com/pronoiac/tarsnap-cron - which might be helpful to someone else. It splits up the archiving and the pruning of old archives, so you can do those with different keys. This part is as yet untested. It probably requires an tarsnap fsck if you do those on different systems. I was going to forgo the plug, but it might be helpful, and I'm about to get some sleep, so I'll probably miss the best time to contribute to the discussion.
[1] https://github.com/pronoiac/tarsnap-cron - which might be helpful to someone else. It splits up the archiving and the pruning of old archives, so you can do those with different keys. This part is as yet untested. It probably requires an tarsnap fsck if you do those on different systems. I was going to forgo the plug, but it might be helpful, and I'm about to get some sleep, so I'll probably miss the best time to contribute to the discussion.