What I would absolutely love to try is what Motorola did for their Moto F3 phone. The F3 uses an E-Ink display like the kindle but as you can see from the pic, it is also lighted from the sides of the screen.
I am thinking about a custom case with a piece of sturdy clear plastic to cover the screen and deflect light from the top or sides onto the screen. I've got spring break this week so I'll draw something up and maybe start building.