What I see is that Neil’s daughter saw a single Missouri Confederate uniform uniform button and he threw out the comment as to the ability to identify the soldier who wore it and made comment as that investigation would be like finding a needle in a hay stack.
I agree with that conclusion and with that, drop the matter.
Note, over 52,000 soldiers are found in Missouri units, see:
The museum staff might have records of where and when this button was found which could narrow the search somewhat. But still, an emense hay stack!