Mrs. Bennet has had five babies in quick succession and the older two need more attention than she can give (Elizabeth especially might have been a handful). Practical, levelheaded Charlotte would have been a perfect older-sister figure for them.

Very plausible idea!
Regarding the Lucases I wonder if perhaps there is at least one lad old enough to stand up with a girl dancing. This is contradicted by the fact that we never hear Mrs Bennet having any designs in that direction. I have forgotten what Sir William is worth.
(Chapter 6 ... Mary ...was glad to purchase praise and gratitude by Scotch and irish airs, at the request of her younger sisters, who with some of the Lucases and two or three officers joined eagerly in dancing at one end of the room.)
Now Kitty, Lydia and one Miss Lucas (Maria. Charlotte wouldn't join would she?) would need three gentlemen. If there is yet another sister they need one more male partner. But if there is a brother willing to dance could that be the same young boy who boasted about drinking wine by the bottle? If not there are at least two boys and two girls in the family.