As a hobby project, I’d like to rebuild my (admittedly rarely-used) Librem 13 with a “from scratch” Linux distro, mostly to improve my understanding of Linux.
There are projects like this, for example: http://www.buildyourownlinux.com/
Are there any particular pitfalls to watch out for when doing this with the Librem? What’s the best way to get started with such a project? I don’t want to just wipe the thing and get lost, of course. 
backup, always backup or use a different hard drive for experiments 
It is a very very good project.
To tackle that without any fear of crashing it all I would first learn how to completely install a fresh PureOS on my Librem.
You’ll know then that whatever happen during you experimentation you will always be good at reverting to a clean state.
It is always a good skill to have anyway.
PureOS installation is documented on puri.sm.
After that experimenting with LFS will be even more rewarding considering that OS installation from a validated release is level 1 and LFS is level 2 to …
Since it wasn’t mentioned in the text of your post, perhaps you aren’t aware that Linux From Scratch is a real project.
You could always set up a virtual machine to try things in, and if your mess things up in the virtual machine, it’s no big deal, you can just revert to a previous state or wipe it and start over, without any risk to your actual OS.
That’s a good idea—I think I will start with:
We’ll see when I get around to toying with this.
Yup—LinuxFromScratch was actually the first thing I came across, but I forgot the name, and came across BYOL when I made the original post. Doing my first tries at building a Linux in a VM is definitely a good idea. Thanks!