I wrote a CLI updater for linux, and then ported it (I think, I'm not a Mac person) to OSX. Check it out here:
https://github.com/eli-schwartz/calibre-installer/
It's run as a launchd task, just like on linux I use a systemd timer.
If you can test it and it works as expected, I would be totally OK with having it linked as an alternative method in the OP.
Or feel free to loot my methodology for ideas, e.g. checking for updated versions.
P.S. Take a look at how I installed the command-line tools. Well worth doing IMHO.