Okay, so looking at the Stone Wall (and Marye's Heights as a whole) as a tactical problem, using contemporary tools.
The first thing to note is that the frontage from the river (around Dr. Taylor's) to the unfinished railroad and Hazel Run is about 2.5 miles - that is, it's about 13,000 feet. This means that very roughly speaking a two-deep line is 13,000 men.
As things kick off, Anderson (7,600 CS PFD), McLaws (8,000) and Ransom (3,900) are in that sector, though McLaws and Ransom are concentrated at Marye's Heights itself. That means that the Heights are extremely dense - I believe there's a quote about a quintuple line at the wall.
Any attack that might succeed needs mass. Attacks need momentum and density if they're going to continue through the beaten zone to reach close quarters; if the Union troops can reach close quarters then they're likely to succeed, the problem is getting there (and of course mass exposes more men to Confederate fire, though the historical piecemeal attacks did that anyway). Honestly a better approach is going to be to cannonade the works along the rest of Marye's Heights, but let's say for now that destroying the works isn't an option and that all the artillery is doing is counter-battery; fortunately the Union has over 300 guns so they should be able to conduct effective counter-battery.
The first obstacle is the ditch canal. On the Confederate left the main canal is close to the Confederate main line of resistance; further south around Marye's Heights, though, the ditch canal is several hundred yards (400 yards or so at closest approach) from the Confederate main line of resistance, and so the canal is an obstacle that isn't covered by the full power of the Confederate defences. It can be passed and the Union units form up on the far side of it.
Taking for now that the Union main attack will be with about 40,000 effectives, while another division or so is facing Anderson to the north, the frontage from the Washington Monument to the Hazel Run is just over a mile (and so a two-deep line would consume about 7,000 effectives).
The Napoleonic-French doctrinally correct approach here would be to push forwards a thick line of skirmishers to engage the wall at all points (and take control of farmhouses near the wall), while brigade columns (probably consisting of columns of double companies at half or quarter distance) pushed forwards to strike the Confederate defences; these columns would be good targets for musketry, but they'd also have the momentum and speed to push through the beaten zone relatively quickly and in effect each one needs to be beaten individually (but at the same time) for the Confederates to succeed. One of these columns should follow the unfinished RR and come up on the southern side of the Heights themselves, then turn north and cut in behind the Confederate position.
Notional structure with 12 brigade columns advancing (4 divisions) behind the cover of 2 divisions of skirmishers. Since the columns are comparatively dense they have momentum and, importantly, they can follow the easier terrain.
This wouldn't necessarily work. The position is strong. But this is how it would be done if you were trying to do it properly (i.e. in accordance with principles of mass using tactical methods which already existed at the time).