Chosen Solution

As the question title states, I’m looking for suggestions on how to remove the button from the case of a Moto 360 2nd Gen (42mm). I’ve tried tweezers (both a friend’s iFixit set and a professional phone repair place; end result was tweezers bent, and button didn’t budge), fine tip flat tip screwdriver (no dice). Anyone have any suggestions on where to find the 6 lug spanner/spindle nut (not sure of what it’s called exactly) that fits the button, or anything that might grip it snugly enough to back out the button? My inability to back out the button is holding me up from replacing the battery. Thanks. :)

In my toolbox was nothing to fit in those small holes, so I had to find an alternative way: My solution was to pull the cover ring a bit out, but only so much that it would hold the inner cylinder. Then turn it around with a flat pliers (dont know if thats the correct word, but any pliers will do the job). And it worked. Ok, there is a risk that the ring will break, but mine ended up with no scraches or any marks. Maybe you can put something between the ring and the case, so that it is less fiddly to hold it there and give the pliers some tape so that you dont get scraches for sure. But otherwise its the best way I have found.

I was actually finally able to back out the button using a 6mm 2-pin spanner bit that seemed to fit well enough into two of the pin holes. However, while I consider my question resolved, as ultimately I only really wanted to be able to fix my watch, it would still be nice to be able to find the proper tool for this task if it exists somewhere, as someone else may benefit from it. But my watch is now running on the replacement battery from iFixit, and all seems to be well so far; time will tell if my battery life issues have been addressed.

Motorola Moto 360 2nd Gen Motherboard Replacement - iFixit Repair Guide