S380 balance not quite right
I don't see any difference between these parts that would affect the balance's function. You're showing the two top attachments, and for all intents and purposes they are identical. Could it be the difference lies in the bottom attachment?
Does that make sense?
The pictures in your first post are the top attachment, not the bottom shoe. These are meant to face up when you install the balance. If you have these on the bottom when you're installing the balance, then it's upside-down.
The size of the top attachment shouldn't account for that wiggle you describe. A 1/8" difference isn't really that much. This is because the bottom shoe is what keeps the balance firmly in place; all the top attachment does is catch the top sash guide. That's its only function, and it's why you can get away with a slight difference in size.
If your new balances wiggle, then the bottom shoe is likely the problem. I would compare the dimensions of the bottom shoes to confirm.