Pick up a copy of Avalon Hill's [The Guns of August] and see how well it works.

( The Guns of August )

At a glance, I'd say you're neglecting to account for the Balkin theater, which was after all the touchpoint of the war.

...but you could just be leaving out all those forces for simplicity's sake.

ugh, I think I found a question with an accepted answer that is wrong(-ish) and Durden's answer is actually more correct

It happens. A much bigger upvote total is usually (for me at least) a big tip-off.

@T.E.D. Thanks for pointing that out, I've never heard of that game, I look forward to getting it!