Now I found the third coin cell to be dead after around 10 days

I was checking for the dead battery somewhat infrequently by the way, so I think it's very likely the previous 2 also didn't survive much longer than that...
The coin cell has no where near the capacity of the original Ni-MH cell.
I'm actually not entirely convinced of that, here's someone's original (leaked) battery from shmups forum:
https://shmups.system11.org/viewtopic.php?p=846242&sid=028b7cf5b884c14aa8884f9eeede16bc#p846242
... and it's 60mAh. Internet tells me that a typical CR2032 should have 235mAh capacity, so it should be better?
Anyway, I kinda don't want to wait at least 10 days again to see what happens, so out of curiosity I thought I'd try to measure the battery draw by putting my cheap multimeter in series:
It seems to measure around 1.8mA when the motherboard is off (it shows 0 when it's on). If we take that 235mAh figure then that's 235/1.8 = 130 hours, so like 5.5 days... who knows what's the true capacity of that battery and this meter isn't the greatest but we're in the right ballpark at least, so I'm somewhat convinced that I didn't just get 3 shit batteries in a row and this really will not survive for very long. If you see a fault in that metodology let me know
I would be curious to see if anyone else with the coin cell mod could try to repeat this? Is this an expected current draw or maybe there really is something faulty somewhere in the battery circuit that causes this? Not gonna lie, if that's the expected result then this solution is just kinda lousy - I can sometimes go more than 2 weeks without powering up my PGM, so there's probably no point in trying to keep my high scores saved
