The rfid-looking antenna is bluetooth.

Per the teardown guide, Fitbit charge HR Disassembly, the battery is 031420, or 3mm x 14mm x 20mm.

The batteries took about five weeks to arrive, but did the trick. Fitbit reassembled and is now fully-charged.

One thought is the number on the front is the manufacturer ("LSSP") and dimensions ("031420") of the battery. (For example, see here: http://www.gmbattery.com/product/showpro...)

Using this link, the model "GMB301320" (at 45 mAh) would be close.

I ended up using a combination of the T3, H0.7 and H0.9 bits from the tool kit to get the screws out. Neither was a perfect match, though.

I also added three photos showing the next steps of disassembly.