The Pebble Time Round has a lot of problems with battery bulge - pushing the frame away from the watch because of an expanding battery. Here is a known source of working batteries (with a catch.) The problem is that you have to modify the battery connectors to get it to work properly, but a Pebble Junkie has proved that this battery does work!
We’re still looking for battery distributors, but now we actually know what model batteries are inside, thanks to Hugo Telmo Silva. Click here to see photo of battery and connector. If anyone can help locate a battery source, let me know!