[twl] has a board that does just that, converting HDMI to something these displays can understand, and providing a framebuffer so these displays can be written to through small microcontrollers.
If you go this route, look for a switch that lets you plug in up to four devices on one HDMI port. While two HDMI inputs are better than one, having only two connections puts you in the same boat ...
You can find it in low-end cellphones, and a single board Linux computer without HDMI ... in this protocol that’s in everything with an HDMI port. [Joshua]’s work is based off a talk by ...