I think the key is in the 5th generation iPod touch. It is an iPad 2/iPhone 4s-class device, processor-wise (with a lower-quality camera and a higher-quality display).
What if the iPad mini was the same device as the 5th generation iPod touch?
Same internals, cheaper (non-retina) display traded for a larger battery.
I mean: identical boards and chipsets internally for all but power and display/touch surface management…