If you are looking for something for those purposes, some e-readers used rootable android as their OS, which would make displaying custom stuff relatively easy.
do you know of which ones exactly? I was looking into using an old kindle for such a think, but couldn't figure out a straightforward way of pushing data onto it
For devices which do have a VNC viewer, is it possible to periodically (e.g. every 15 mins) wake up the device, refresh the screen via VNC, then power off or switch into very low power state running only the timer?