My understanding is that if you simply turn the brightness on an LCD display down to whatever the ambient brightness is (hold a piece of white paper next to the screen to compare), that there is zero eyestrain over what paper or e-ink would be.
Have you tried that? It feels strange at first -- as if the screen feels "dim" -- but then once you realize the contrast is just fine, you get used to it within minutes.
(And in case you have a problem with glare, just get a matte screen covering, easy peasy.)