I had very little success with the Freescale tools, nor with the k3flasher utility. Either the PC wouldn't recognize the Kindle, or I'd get mixed (and varied) error messages.
I put the whole thing on hold for a while, but yesterday I decided to have another look. I took it apart (again), but this time with a voltmeter and oscilloscope at the ready, to see what's happening. The first thing I checked was the battery, and to my great surprise there was no voltage whatsoever between the + and - terminals. Surely that can't be normal? (I've started a
thread in the Dev Corner, which seems more suitable for that level of detail.)