I think it unlikely that McClellan takes Richmond before fall 1862. He may establish a siege of Richmond, but he won't know how to complete the attack. It took Grant ten months to take Richmond (from the start of the siege of Petersburg). How does McClellan do it any faster?
From the battle of Seven Pines (31 May) to Lee's attack at Mechanicsville (25 June) McClellan made no significant advance. Leave Johnston in command, and what changes?
After Seven Pines, McClellan abandoned any thought of fighting his way into Richmond, and instead decided to use heavy siege artillery to breach the defenses. (But he was still preparing this at the end of June.)
We'll suppose that after Seven Pines, Johnston makes no more counterattacks, but digs in from Chaffin's Bluff on the James to the Chickahominy near Mechanicsville. McClellan brings up his guns, and starts bombarding. Nothing happens, except a few men are killed on each side. Maybe, if McClellan really masses the siege guns, he can force the Confederates back a few hundred yards at a time, across a few hundred yards of front, with each push taking a week to set up and execute. (If it's possible at all. There is no evidence from the Civil War of anyone doing this successfully. Fortifications either fell to assault or to starvation.)
Richmond is five miles to the rear, and the front is about eight miles wide. That means forty square miles to take, in bites of maybe a quarter square mile - 160 weeks. Now obviously when the line is pushed back far enough in one sector, that can force additional withdrawals, so divide that by four. That still means forty weeks.
Lincoln will get frustrated, and propose the EP (or a variant). If Richmond has not fallen by January 1863, it will be ignored by the South, and will come into effect.