FYI, the closest batteries I have found so far are 3.7v 605065 2800mAh packs. The extra 1mm in either direction is a snug fit, but works fine. You can pick these up for 10-12$ each on Amazon (you want 2) or less on other sites.
This is using the original battery connector + the board and temp sensor.
So far so good. I haven't had any charging issues. The only quirk is that the battery level maxes out around 75%.