Too many times of whirling the Nook around on the 1/4-20 microphone mount finally broke the bond on the T-nut inside.
The JB Weld sticks fine to the steel of the T-Nut but not so well to the inside of the back cover of the Nook.
I decided to do some lightweight reinforcement of the back cover.
I took a piece of 1/64" thick sheet aluminum.
That's thick enough that you should use sheet metal snips to cut them
but you could use a good pair of paper scissors (as long as they're not yours).
I cut a piece as big as the battery compartment, about 2-1/4" x 3-9/16".
I drilled a hole in the right place.
I gooped epoxy on the underside of the aluminum plate.
I gooped epoxy on the underside of the T-nut and pushed it through the aluminum and the case.
I set a screw and a little cup on the outside to provide tension, then reassembled.
The next day I removed the screw and tried it out.
It's much stiffer and a lot less wobbly than it was originally. Success.