I have been dreaming of having an E-Ink Android tablet or e-reader that could run the Logos app and other text-intensive apps. Well, the time may be upon us! Check out www.meetearl.com. Earl is an E-ink Android tablet that runs Android 4.1. It has all the usual Android tablet features, including a backlight for the display. But it's also designed for use outdoors, on hikes and such, so it has GPS, maps, a radio, and can give you your weather (including temp, humidity, wind speed and dew point). It's a little more expensive than your average Android tablet or e-reader, at $299, but for all it can do, it's a bargain - especially if you love the outdoors. It's not yet ready for shipping, but may be later this spring.
Another option, for those who have the Kobo Aura HD, is a hack that allows you to run Android 2.3 off a microSD card. The info is here:http://angor00.blogspot.ru/2014/02/booting-android-from-external-sd-on.html
I believe that Logos and E-Ink would make a great team. E-Ink is easier on the eyes than an LCD or similar display. If neither of the above options appeals to you, encourage other companies, like Nook or Kindle or Kobo, to offer such a device. The Nook e-readers run Android, but 2.1, too "old" for Logos even if you root the device.
Also, if Earl and any other such devices are successful, perhaps Logos could tweak the app to look even better on an E-Ink screen.