Picked up a few of the six buck pinty's, probably like most others here, just because.
Seemed odd to put such a small/odd 1620 battery in there considering the overall cavity is typical of 2032 size and turns out the only limiting factor is the threaded ring surrounding it.
Unfortunately the wrench slots prevent the oem ring from being opened up enough without breaking it in half so I popped out a few larger id rings on the lathe and a 2032 fits in there just fine. Because I can, I guess...
FYI for anyone wanting to do same, I don't have metric threading gears on my lathe so found that 32tpi worked fine as opposed to the .8mm pitch of the original.