Possible Earlier PoDs
The consensus opinion I have found, after reading many Civil War threads over the past n years, is that if McClellan wins the election due to an 1864 PoD, the Union will still be restored, because by the time he actually takes office the war will be so close to being won that he cannot reasonably keep up a "Peace with Separation" stance.
In line with that, I say a PoD earlier in the war is required, compared to the Atlanta-Mobile-Shenandoah suggestions or the Early-taking-Washington suggestions of the last several pages. If the course of the war changes earlier on, the Confederacy can get a better chance of surviving.
The first possibilities to come to mind (there are many others) include:
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Fort Donelson. Grant and company will still take the fort. However, if Floyd and Pillow act even a smidgen less incompetently than they did historically, the Confederates do not surrender. Recall in OTL that their first breakout attempt was very successful in disrupting Grant's siege line, the Confederates withdrew of their own (commander's) volition and were not forced back, and even once the line was reestablished some thousand troops still escaped with Forrest. If the Confederates make *any* effort to hold the line open once they have got it, the whole of the 10,000 troops escape.
These troops will join A.S.Johnston in his concentration of forces. With 10,000 extra men at alt-Shiloh Johnston/Beauregard have the chance (not a certainly, but easily a coin flip) of severely roughing up if not destroying large chunks of Grant's army. The resulting better numerical balance, plus Grant being disgraced, gives the Confederates a fighting chance to survive until March 1865.
Glendale. Also known as Day 6 of the 7 Days. McClellan was busy moving his forces southward to their 'final' position at Malvern Hill, but today they were slowed at a bottleneck where several roads came together at Glendale. Several Union divisions were hard-pressed by Longstreet and half the Confederate army from the west. Meanwhile elements of the VI (I think) corps defended approaches from the north across White Oak Swamp. These men were severely outnumbered by Jackson with the other half of the Confederate army, but for unexplained reasons (possibly extreme tiredness due to lack of sleep) Jackson never strongly pressed the attack. If Jackson acted *remotely* with his usual aggressiveness he would easily have pushed the Union defenders back and come up behind the main Union line at Glendale (as detailed in the "What If?" anthology").
This force, consisting of around half of the Army of the Potomac, would then be surrounded and outnumbered by Confederates. Any large proportion of them that do not surrender will escape only by being routed completely. Depending on exactly how many troops are lost, and how disorganized the Confederates are in victory, Lee may press his advantage, and may have a non-negligible (though still small) chance of overrunning the new Union line at Malvern Hill. If Lee, burdened by the prisoners, holds off and lets McClellan escape, this is even better, as McClellan is thoroughly disgraced, morale in the AotP plummets with Confederate morale rising in proportion. Force-wise, this frees Lee much more quickly to move to northern Virginia to counter the threat from John Pope when it appears, and with possibly fewer (or no) reinforcements from the AotP at alt-2nd Bull Run, Lee may have a numerical superiority, able to score another large prisoner haul there. The resulting closer numerical balance heading into late summer of 1862 gives the Confederates a fighting chance in the Maryland Campaign.
Stones River. In OTL, Bragg nearly managed to swing his attack entirely clockwise around Rosecrans' lines, trapping the Union army against Stone's River. Rosecrans held Bragg off of his 1 supply line by the skin of his teeth using at one point his Engineer Brigade and reinforcements arriving just in time from his opposite flank fording the river. All of this was made possible by Rosecrans' presence in person to get these troops to the right spot in time. If Rosecrans is impeded in *any* way, the Confederate advance can get around the Union flank.
The Confederates do not have enough men to completely encircle the Union line. Nevertheless, they will clearly have the better tactical and strategic position and no reason to retreat (which Bragg was loathe to do in OTL after fighting a considerably worse battle). With the numerically and qualitatively superior Confederate cavalry running amok everywhere between Stone's River and Nashville, the onus is on Rosecrans to attack and break the Confederate's lines to reestablish his supply line. This attack will *probably* be successful, but not without costing the Union far more men proportionally than the Confederates will suffer. In turn, Rosecrans retires to Nashville to rest and refit, and Rosecrans' aura of greatness (which he did have, believe it or not, in OTL having never suffered a true defeat, and against often superior Confederate numbers no less, until Chickamauga) will be shattered. Already on the ropes with the administration, Halleck/Stanton/the rest will be even slower than OTL to resupply Rosecrans' army (if they don't replace him entirely), so he starts the Summer 1863 campaign with fewer men, worse supplies, and all the way back at Nashville. Even if he can make any progress at that point, Confederate reinforcements coming for alt-Chickamauga are fighting further north and can hold a line at or north of Chattanooga, preserving the rail line and East Tennessee while they are at it.
Chickamauga. The Confederates got a victory at this battle anyway, but they could not significantly destroy the Union army, which was what was required at this point. However, as I have detailed in a past thread (
https://www.alternatehistory.com/discussion/showthread.php?p=4400374#post4400374), if John Bell Hood is *not wounded* at the height of his breakthrough in OTL, the Confederate advance maintains its cohesion. It is eminently possible to capture a third of Rosecrans' force, and kill/wound/put out of action another third, while Bragg suffers no more than OTL casualties.
With only ~20,000 defenders against a revitalized and sky-high-morale Confederate army, Rosecrans cannot hold Chattanooga for more than a couple of days. After Bragg re-secures the city, he can stop and wait for Longstreet's/Johnston's supplies to catch up to their troops. With an actual victory, and Bragg having 'listened' to his subordinates in seizing the city, there is no October mutiny. A *slightly* more harmonious Confederate high command actually fortifies Lookout Mountain and beyond against a time when Rosecrans/other Union commander returns, having learned their lesson since August and unlike OTL being in a position to actually do something about it. If Grant is put in charge of a concentration of forces to oppose Bragg, he is starting many miles further west, and with 20,000 fewer troops. If Longstreet is kept with the Confederate army, it is entirely possible that Grant can have a signal defeat attacking strong Confederate positions. If Longstreet is absent in East Tennessee, he now actually has time (and a somewhat more cooperative Bragg sending supplies) to make a real campaign to re-take Knoxville. Whichever scenario plays out, it is unlikely at best that Atlanta will fall before the 1864 elections, and if it does fall in time for a Democrat's inauguration there will not be time for a Union advanced *past* the city.
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Give me time; I'll think of some more if required.