I get that the intent is to represent the feeing and spirit more than the exact 1-for-1 numbers and regulations, but I don't quite see how 3 regiments emerges to that end? 4 regiments per brigade seems like a closer representation to me, with maybe high army org increasing that to 5. 4k troops in 4 regiments seems to be about the ideal authorised strength from what I understand, and particularly once you account for overstuffing or auxiliary units having 4 regiment slots per brigade seems like about the right representation to me. Also allows for more reasonably combining all command-level assets into 1 brigade, which also seems reasonable to me. Just a thought, though.
Why would you say the Division is missing though? A division is a unit comprised of multiple brigades, usually 3-5 or so, and that is exactly what a player's "corps" is. Manpower-wise, the "corps" in the submod seems to come out to something like 5k men upwards, perhaps dipping into low double digits for some of the biggest ones. That also seems to about match the link you provided (12k authorised, up to half as much in practice), and if we look at, for example, Wikipedia article for 1st Bull Run, most divisions there ranged around the numbers of 6-9k men (with the notable exception of 2nd (Hunter's) Div. at 2.5k). Even the commanding officer for in-game "corps" is brigadier-general, at least when you form them, and that's about the rank for division command, at least in the Union.
All of this to me seems like a really strong case that vanilla corps are in the mod now divisions for all intents and purposes, and are rather accurate representations at that.
Then, since a unit that you get when you combine 2-3-4 division is a corps, I think it follows that the player is now on the whole in charge of a corps, as opposed to a whole army. This last distinction is mostly academic, though, since there isn't much impact on gameplay, and I imagine by the late game you would be able to have 4 or 5 divisions and the border between "a really small corps" and "a really big army" is blurry one anyways.
Just a minor note on grammar btw - as far as I know, "Corps" is both the single and multiple form of the word.
So you write "1 corps, 2 corps, 10 corps" even though you read "One core, two cores, ten cores"
That's what you get when you borrows words from the French I guess