I also struggled with this issue of library books, Overdrive, and ADE. I like to read in bed without having to turn the light on, so thought I needed to get the book on the LCD side.

When that didn't work for me, I downloaded Flashlight from Amazon Apps. Now I can turn on the flashlight on the LCD side and it lights up the eInk side so I can read my eInk book without an extra light.

For me, it is actually more comfortable holding the book open like a regular book than folding to tablet anyway. I'm assuming/hoping that the Flashlight doesn't use any more power than having the book open on the LCD side, but haven't tested to find out.