For awhile, I have been oggling at the Lenovo Vibe X3.
5.5"
NFC, OTG, BT 4.1
Android 5.1 (Vibe UI)
Snapdragon 808
FHD IPS Display
Notification LED
Dolby Atmos, Forward Facing Stereo Speakers
3GB RAM, 32/64 GB ROM (Also expandable via hybrid sim tray)
Camera is decent..but lacks Optical Image Stabilization
It's slightly above $400 on Amazon (for the 32gb variant).

Root is (theoretically) possible, XDA said it's source code has been officially released.

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IMO, having OTG or a BT Keyboard will be acceptable as the main keyboard.
I actually have one of those Rii Mini wireless keyboards with wireless reciever, I use it via otg.
BUT I'd recommend finding a backlit model. Its a pain when typing in the dark.