I habe a "Pocketbook Verse Pro" that runs Linux. No need to root, you can copy ARM executables to the SD card and run them (that's how I use Syncthing on it). KOReader also works on it.

+1 for the PocketBook. I have an Era and use it with KOReader and Calibre. Installation was as easy as copying a folder onto the device.

I also wrote a short write-up about my experience with PocketBook devices and KOReader, for anyone who's interested: https://tc3.eu/posts/pocketbook-era-with-koreader/