Previously, someone posted about a battery they found that snuggly fits in the Zune HD. The method he used to get it to work with the Zune is the same that I'd been using all this time: swapping battery PCBs. This method is bad for the battery because of how much heat all of the soldering creates and gets absorbed by the battery cell. The battery gets soldered to 4 times.

This new method only requires soldering to the battery just 1 time.

Here's my parts (with battery being the one that the other guy found)

Battery (750mAh) - $8.99: Liter 3.7V 750mAh 403450 Lipo... https://www.amazon.com/dp/B09FLDRYQ5?ref=ppx_pop_mob_ap_share

Thermistor (10k Ohm) - $7.49: uxcell 20PCS NTC Thermistors... https://www.amazon.com/dp/B07P5QC26X?ref=ppx_pop_mob_ap_share