I don't have specific torque values, I just got the screws decently tight by hand and haven't had an issue with them coming loose. You could always add a bit of of thread locker to the screws before reinstalling them. Make sure you use the removal type in case you need to open the watch back up.

Please take note of how much of the top face of the standoff is visible in each photo. The plastic tab sticking out from the battery should be resting directly on top of the standoff (good photo) and very little of the standoff top face is vidible. The bad photo shows a clear gap between the tab and the standoff and you can see much more of the top face of the standoff. It may be helpful to examine the placement of the main battery prior to removing it to establish a baseline of what correct position looks like.

The Amazon item is compatible with gen 6, it just doesn't say so in the description. I have installed that item in my own gen 6 Thinkpad and it has been functioning without issue.