It's not about being un-coordinated, it's about free will. Someone chooses a particular regiment because they share a particular nationality, or maybe they've traced their family tree, or there is their namesake in that regiment, or some other connection that is just as varied as the people.

And then they come together and only some of them match and not everyone has that many spares. We've had an infantry regiment on the field before and the artillery was a different regiment.

I remember correctly, there was one time there were 4 of us Rebs with 1 of them as a sentry on the cannon and he was attacked by 3 Union, so he came back to camp and got us.
Then us 4 went back up the hill and retook the cannon, of us four, 2 were from one regiment and the other 2 from somewhere else and no one was artillery.
We showed a skirmish at best with albeit a fraction of the troops that would actually have been involved.

We do not have the members, money, equipment, supplies, events or resources to lay on something accurately.
I like your reply but it is somewhat romantic, fantastical even as far as we can go.
No offense inferred.

As far as OP is concerned, make sure you get the right stuff first and a Zouave musket is wrong, but we cannot afford to be picky like you.
And that is understandable as it is your history. If people here were told, We are re-enacting this particular thing and nothing else, then a lot of people wouldn't do it at all.
It's bad enough when the WW2 starts up and we lose most of our audience, people like the bangs.

I assumed OP was here as he was asking about that particular musket and as an American he wouldn't make that mistake anyway.