I ordered the second one and got it earlier this week. It does work, I charged up a totally dead battery over a period of about 24 hours. It's not the best fit, but absent a better solution, it works. I'm attaching some photos of the charger with the battery and a photo showing the actual size of the battery. As you can see, the battery is quite large for a flat battery, but then there's plenty of room inside the Kindle. I can tell you that you have to put it some place where it doesn't get jostled because the contact between the battery and the charger are not real tight which allows the position to shift just enough to cause it to stop charging.
https://www.flickr.com/photos/aweaton/14361404842/
https://www.flickr.com/photos/aweaton/14176275859/