Something I would like to mention before this thread gets to old is, could a alt Fredericksburg work? Like if Meade had been supported when his division had taken part of the southern rebel line the whole battle could have been won then, couldn't McClellan do better? He has more troops then burnside did, and at lest to start with (before Johnston gets his reinforcements) the Confederatecy less then the OTL Fredericksburg.
Well, going for the "cross before the area is defended" won't work because there's two divisions there at the start, so it'd have to be much the same "slowly build the pontoons" as historical, which gives time for the Confederate reinforcements to arrive. (It helps that an attack on Fredericksburg was exactly what Johnston was expecting, of course)
Johnston has access to:
Immediately available at Fredericksburg: 7 brigades (minimum 6)
Whiting's division of 3 bdes (Whiting, Hood and Hampton)
Holmes' division of 4 bdes (French, Walker*, Field and SR Anderson)
Available elsewhere on the Rapidan/Rappahanock line: 14 brigades (minimum 13)
GW Smith's division (GT Anderson, Wilcox* and Toombs)
Longstreet's division of 3 bdes (AP Hill, DR Jones and Pickett, with DR Jones being senior and commanding the division in lieu of Longstreet's assuming a "corps")
Ewell's division (Elzey, Trimble and Taylor)
Early's division of 3 bdes (Early, Rodes and Kershaw)
DH Hill's new division assembled from two slack brigades (Griffith and GB Anderson)
* pulled out to help form central CS reserve
On top of that Gregg, Branch and JR Anderson from the NC force were sent to Northern Virginia when McClellan made his historical move, along with Cobb (who'd been pulled from the Peninsula) being released back to the Peninsula and Colston and Pryor (from Norfolk) going to the Peninsula.
That means Johnston would have:
19 brigades already along the Rapidan/Rappahanock
+ 2 released back to him
+ 3 from NC
+ 1 from Peninsula
+ 2 from Norfolk
Total 27 brigades
Jackson is still in the Valley.
Assuming both sides concentrate everything aside from their Valley forces at Fredericksburg (and that McClellan gets to keep all 12 divisions of his main field force, which historically he did not) then that's about 4:3 in favour of the Union (assuming the strength of the brigades is comparable). Might be workable, but not in "will definitely succeed" territory, especially since none of the DCs or CCs has much if any experience.
If a division is ordered to Fremont, or one is held back to defend Washington along the Culpeper-Manassas-Washington or Manassas Gap - Manassas - Washington approach route, then the numerical superiority erodes fast.