Hmm, .06A/neopixel at full white * 64 neopixels/face * 5 faces = 19.2A.
.06A x 64 LEDs = 3.84A/face
Seems you a little short on power.
Switch between supply and battery, done simply with diode separation, diode each from supply and from battery going to common supply point on a face, higher voltage source blocks out the lower voltage source.
Might want a separate battery/face to cut down on current coming from each battery and to reduce the size/cost of the batteries and diodes.