What strikes me, though, is that if those numbers are correct, it seems like such a very small number of field guns for armies the size that were in play during the Civil War.
I'm glad you said it, because I was sure thinking it! Maybe someday I'll be a Civil War expert, but for now, I'm just workin' on it. In documentaries and movies, you always see a lot of artillery in battles, but from what you wrote, it sounds like either the role of field artillery was played up more than reality or else the field guns were maybe used to a far greater degree in large battles than anywhere else (which would sort of make sense, I guess).
Or perhaps, due to the nature of the transportation networks of the time, fighting was generally concentrated in small areas at any one time, so the field artillery could be moved to where it was needed.
I can see that I have much reading to do this winter.