So... after months I finally have a little time to think about tinkering with my metawears and I discover that one of my two batteries is now 'fat' and sort of squishy! I'm going to assume using it would be dangerous
That is a battery failure, please dispose of it appropriately; this is extremely dangerous! A battery that is "fat and squishy" has permanently failed and can catch fire at any time.
Please have a sand bath nearby in case of combustion and seek the proper authorities to dispose of the battery.
Battery failures are about 1 in a million and there is no way to avoid them. Because it is a chemical system it is bound to fail occasionally; especially when rough-handled or exposed to extreme stress and conditions.
You can buy new/replacement polymer batteries on Amazon or places like Adafruit.
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"especially when rough-handled or exposed to extreme stress and conditions."