Check my comment on the teardown… Fitbit Flex Teardown I think you can find a suitable 031012 battery if you look around & are willing to try dismantling it (which may destroy it).
It's time to speak out for your right to repair
We have a chance to guarantee our right to repair electronic
equipment—like smartphones, computers, and even farm equipment. This is a once-in-a-generation
chance to protect local repair jobs—the corner mom-and-pop repair shops that
keep getting squeezed out by manufacturers.
Join the cause and tell your state representative to support Right to Repair. Tell them you believe repair should be fair, affordable, and accessible. Stand up for your right to repair!