Woo hoo! Checked the mail and my new battery had arrived. $3.89 delivered. I ordered the one from the ebay link in the thread posted by notgod.
The original says
BAK 323036P
9G05 1.07Wh
3.7V 290mAh
The new one says
BAK 363830P ST
9G10 1.22Wh
3.7V 330mAh
Physical dimensions are the same as the old battery except the terminals are on the long edge. This makes me question the accuracy of the rating since the energy storage portion is smaller than the original but I’m not going to be picky. In typical “Hong Kong” fashion, the battery delivered is not same configuration as the one pictured. Fortunately, what was delivered is closer to the origina Clip+ battery. 3 wires (red, black, blue). I’d saved the board off the original battery to transplant to the new one but I took a shot and connected the new battery as-is.
So far, so good. It turned on and resumed playing from where it left off. I plugged it into a computer and it registered 79% and the charging indicator showed that it was charging the entire time it was plugged in. Unplugged it and it’s still working, behavior totally normal. I still need to leave it plugged in to make sure charging shuts off properly but, so far, I’m giving it a thumbs-up.