I might be misunderstanding your comment but the display is run/powered by the board so all you need to do is provide power to the board. For e-ink it uses no power to "hold" an image, only to write/refresh (sorry if I'm telling you something you already know!).
So reiterate, with a 2000mAh lipo battery I should be able to drive the board _and_ the screen for over 3 years if I only refresh it at most once every 4 hours (with "push" capabilities, I don't have to deep-sleep the board to get that battery life). At least, that's what the calculator says, I _just_ got my hardware to play with and so I can't speak from experience. Unfortunately my board is not charging the battery so I need to get a replacement which will probably take a week or two to get here.
Yeah no we're aligned; I have some raspis that I'm interested in doing long term battery stuff with (remote sensing and the like) and it definitely does seem like connectivity is the huge killer, like even if you wake up only periodically to take a reading or update an epaper display, the cost in battery just to negotiate a wifi connection and do tcpip and http things is awful.