LiPo Over Discharged

The ZERO is very similar to the MKR1000 and I haven't seen your issue on any of my LIPO batteries (750 to 1500 mAh)

The only issue I did see was with one out of a batch from China that simply did not charge from the get go using any type of LIPO charger.

I trust your findings but wonder what your ZERO says about it ?
There is a battery test sketch for them.
Maybe pointless but you never know.