GalliumOS is great but sadly it's no longer maintained. I think you can get most of the same benefits with a vanilla distro, but you have to be willing to do the tweaking yourself.
I installed Arch on a CB3-111 last week, and it seems to work fine. I will probably make it swap to zram, and see if I can install a better touchpad driver, but the other limitations aren't things I can fix, most importantly:
- only 4GB RAM
- no meta (windows) key, so I'm using alt as the meta key for i3
- function keys are labelled as media keys, so I have to remember which one is F1
But neither GalliumOS nor Arch are a practical solutions for schools today, unless there's an easy way to lock them down and have central management?
Many Chromebooks can have coreboot installed (https://mrchromebox.tech/), turning them into regular PCs.
And since Google bought Neverware, a regular PC can be turned into a Chromebook by installing ChromeOS Flex.