I planned to get a working BMS from (preferably) a non bloated battery to minimize puncture risks.

There's absolutely no insulation from the heatsink and the battery. Microsoft did put a huge chunk of the cooler on top of the battery (I strongly believe it has been done in propose). Nobody with a sane mind would do that but yet, Microsoft did it...

I think that I'll try to solder 18650 cells to the original BMS and see how it goes. If it does well, no need to reverse ingeneer it. If not... I guess I'll have to acquire some knowledge first to do it myself.