Unfortunatelly so far there is no convenient e-ink device out of the box (ie. min 6" display, full Android 4)
This thread should be used for posting any relevant info.
Nook Touch eReader (root needed) - Android 2.1http://community.logos.com/forums/p/36601/274262.aspx#274262
Tolino Shine Reader (root needed) - Andoid 2.3http://community.logos.com/forums/p/80212/561403.aspx#561403
Sony PRS-T1, T2 (root needed) - Android 2.2 (2.3?)http://community.logos.com/forums/p/63763/570149.aspx#570149
Onyx Boox T68 (not released yet) - Android 4 (probably most perspective device for Logos app e-ink)https://onyx-boox.com/coming-soon-e-ink-news/onyx-boox-t-68/http://www.mobileread.com/forums/showthread.php?t=225652&page=3
Onyx M96 e-ink mobile phone - Android 4, but only 4,3" displayhttps://onyx-boox.com/coming-soon-e-ink-news/e-ink-smartphone/http://blog.the-ebook-reader.com/2013/10/16/onyx-readies-android-e-ink-phone-and-android-4-0-onyx-m96-9-7-ereader-video/
Yotaphone - 4,3" display (device is too expensive)fist-gen: http://techcrunch.com/2014/03/19/yota-phone-uk-launch/next gen: http://techcrunch.com/2014/02/23/next-gen-yotaphone/
Onyx Boox T68 - specifications:
https://www.facebook.com/OnyxBooxItalia/photos/a.486852044720575.1073741826.486831211389325/636765379729240/?type=1&theater
I'm pretty sure the Logos app no longer works on Android 2.1 but it's been a while since I looked at it. You might be able to dig up an older version of the Logos app and get by for a while.
I played around with possibilities about a year ago when I got a Nook Touch for $20 on clearance. But for many people the slowness of loading books/apps even rooted on a Nook Touch/Glowlight is not worth the trouble of trying to get it working. It is nice in theory to access Kindle and Nook books on one device. And perhaps worth the trouble if you need to read outside. Otherwise, there are many options under $100 for 7" Android tablets that run the latest or one revision back of the OS and won't be a hassle/stop working whenever something is updated.
I'm pretty sure the Logos app no longer works on Android 2.1 but it's been a while since I looked at it
This is correct
The current release requires Android 2.3 and up