I could imagine a bigger Confederate win on July 1, but what then? More than likely, Meade decides on a retreat to the Pipe Creek line (he considered this even OTL) and take a stand in a defensible position. So most likely the one-day Gettysburg is a "Second Manassas", while Pipe Creek is an "Antietam".
If we set up a "butterfly net" and assume that everything is the same as it was IOTL except that Stonewall Jackson is alive and in command of the Second Corps (I'll assume for the sake of argument that Ewell is a division commander, with Early and Rodes being the other two). Ewell actually did pretty well on July 1, marching to the sound of the guns and pitching in to the Union right flank, which crumbled under the weight of his attack. Jackson probably would have done the same thing. I think his poor performance in the Seven Days was due to sheer physical exhaustion resulting from his exertions in the Shenandoah Campaign, which would not have been a factor here.
So, the question is whether or not Jackson would have done what Ewell failed to do: take the vital hills that would later form the northern portion of the Union line on the second and third day of the battle. For reasons that have never been clear to me, this question has always been fixated on Cemetery Hill, when Culp's Hill was far more likely to fall. Cemetery Hill was defended by fresh Union infantry and considerable artillery, while Culp's Hill was defenseless. And if the Confederates controlled Culp's Hill, the Union position on Cemetery Hill would be fatally compromised. I can certainly see Jackson driving on to either launch an attack in sufficient force to take Cemetery Hill (which might have been successful but would certainly have cost heavy casualties) or realize that Culp's Hill was unoccupied and sent troops to take it.
But, as you point out, what then? IOTL, realizing that the Union position was relatively secure, Meade decided to make a stand at Gettysburg and directed the five uncommitted corps of the Army of the Potomac to converge there. ITTL, with the I Corps and XI Corps battered even beyond what happened IOTL, it seems like that Meade would have gone with his original plan and ordered a defensive position along Pipe Creek, to shield Washington and Baltimore. Only two of the seven corps in the Army of the Potomac had been in action up to that point; the remaining five were still intact and ready to fight. What would Lee do in such a situation? This is the big question for any serious AH scenario of Gettysburg. If Lee had moved forward and attacked the Army of the Potomac at Pipe Creek, it might well have proved a Fredericksburg in reverse - Pickett's Charge tenfold.
But then again, Lee might not have followed the Army of the Potomac towards Pipe Creek. He will have already achieved his chief objective: inflicting a clear battlefield defeat on the enemy army on enemy soil. His attention might have then shifted to his secondary objective: foraging for supplies at the expense of Pennsylvania farmers (a goal which he actually achieved IOTL: the Army of Northern Virginia subsisted for months on the forage it gathered in the Gettysburg Campaign). The Union army, beaten but not that badly battered, would have ventured forth to engage him sooner or later. Lee could not have afforded to move too far to the north, because it would then have been easy for the Army of the Potomac to swing to the west towards the area around Harper's Ferry and cut Lee off from Virginia. Lee would then have had to try to fight his way out, which would mean that the Army of the Potomac would get the opportunity to fight a defensive battle on ground of its own choosing.
If Jackson had been alive and brought about a more complete Confederate victory on July 1, I think that Meade would have pulled back to Pipe Creek and Lee would have spent a few weeks gathering supplies and sending his cavalry to burn bridges and tear up railroads, until the Army of the Potomac began to advance, whereupon Lee would have either tried to find a chance to fight another battle at advantage or would have ducked back into Virginia while he had the chance.
In any case, even a very successful Gettysburg Campaign, from the standpoint of the Confederates, would not have been immediately decisive. But it might have so utterly dislocated the Union war effort that Lincoln would have easily been defeated in the 1864 election and a Peace Democrat elected, which would have changed everything.