The only set of rules I know that is specifically made to scale up and down one full level of command is Bob Cordery's "The Portable Napoleonic Wargame" which is also "generic" enough to the period that it would be easy to modify into any theater. So for rifled muskets, you just add a bit of range, for repeaters you let them shoot twice, whatever. It has Brigade, Division and Corps [and higher] rules. My guess is these would satisfy your needs, and they are cheap enough that if they didn't you can still afford a second set of rules for skirmishing.
A second possibility would be Neil Thomas' "Wargaming 19th Century Europe, 1815-1876" which can easily be pushed BACK, earlier, as 1815 still has Napoleonic fighting. Review here:
http://lonewarriorswa.com/wp-content/uploads/2013/04/Wargaming-19th-Century-Europe-book.pdfBoth of these sets use a base as the key game mechanic, and the number of figs on the base [and the size of the figs] is irrelevent.
A final possibility is Neil Thomas' "Wargaming: An Introduction" which has battalion level rules for napoleonics and ACW, and a very nice set of skirmish rules. Again, the base that he says an individual fig should be on for the skirmish game is size and number of figs neutral - you could easily have a base with several 6mm figs on it and play the skirmish game. It would even make sense as the figures all have multiple hits and take "wounds" before they expire.
I've played the heck out of all of them except the Portable Wargame rules, which also look good and I own.
I have a ton of posts on all the Neil Thomas stuff at my Horse and musket blog here:
https://ecw40mmproject.blogspot.com/which may help give a better feel for what I'm recommending.
But I agree with all the above - you are asking for too much from ONE set of rules - you will almost certainly have to have TWO. But I think PW and WAI would be the two books / rules I'd get.