How are they supposed to win in 1863?
Maybe they can't. But they're not going to have a chance in 1864.
There's no presidential election that year, so unless Lincoln just abdicates, there's no way to force the issue
It's hard to imagine any new President taking office with the intention of going down in history as "The President Who Lost the Civil War." That seems to be against human nature. What would he do for an encore? Publicly castrate himself? Assuming McLellan wins, he's got minimum two, maybe three years, before he would be willing to throw in the towel and accept history's humiliation and national disgrace. The Confederacy has no chance to last that long.
unless you think the Confederacy can just conquer the North outright.
Nope.
They have to make it to Spring 1865 without a major Union army in the Confederate interior,
I'm not going to say ASB.
But....
whereupon the Union will be running out of money, most of their best men's enlistments will have expired, and there could be an armistice that makes mediation possible.
Unfortunately, the Confederacy has already run out of money, of men, of guns and bullets, firepower, shoes and food and just about everything else. There was just no Confederacy left to speak of.
Comparatively, the Union is in no danger of running out of money. The command staff, officer and NCO corps were stable and had refined, their logistics were excellent and their potential manpower reserves are immense.
The Confederacy is not going to win a war of attrition. Period.
You have this romantic notion of a splendid sequence of military victories, but you recognize that these, in themselves just are not enough. So you keep trying to artificially bolt on a mediated resolution or peace settlement dependent on a degree of Union goodwill/incompetence/submission which is irrational.
Furthermore, victories in years prior to 1864 will affect the resources they have in 1864. For example, if Vicksburg doesn't fall, they can still buy supplies in Mexico
With what? The Confederacy was awash in hyperinflation. They had no international credit, and the French weren't going to bankroll them.
and ship them by rail to where they're needed.
Setting aside the problem that the Confederacy did not have a unified or organized rail network, but rather a mismatched series of small independent rail lines which were oriented around serving ports.
If the Kentucky campaign was managed better, they'll be able to recruit out of Nashville and during forays into the bluegrass. If Lee smashed the Army of the Potomac in the Pennsylvania campaign, he wouldn't have to surrender all of Virginia north of the Rappahannock to the Union.
So basically, an entirely different civil war in which the Confederacy, already the recipient of an incredible string of luck in OTL, gets even more incredibly lucky in every possible way.
Okay.
I don't discount the possibility that a man could flip a quarter and have it come up heads 1000 times in a row.
If Lee was facing a smaller (flip-heads), less experienced (flip-heads), less well led (flip-heads), less enthusiastic (flip-heads) Army of the Potomac (all qualities associated with a record of defeat) with a beefier army (flip-heads) led by his best lieutenants (flip-heads), keeping them off the Rappahannock is a possibility.
Each of these individual things would require several hundred or thousand individual decisions to get there. So Lee would need to flip his quarter and have it come up heads about 10,000 times in a row.
Okay.
If Chattanooga is still in Confederate hands in fall of 1864,
flipflipflipflipflip
the Georgia agricultural industrial heartland is safe
What industrial heartland? It's still a tiny fraction of Northern production, and its resource starved.
until McClellan takes office,
In order to promptly go down in history as the man who threw it all away? He's just not going to do it.
especially if Lee bloodies his opponent to the point he can send men or commanders west.
flipflipflipflip
This all seems contingent on an astonishing run of luck which seems improbable, given that the Confederacy was already the beneficiary of an astonishing run of luck to get as far as they did.