My timeline proposal, Mk2 with robcraufurd improvements
December 1861
Two Guinness World Records factoids: Ulysses S. Grant gains the dubious distinction of becoming the first general to die in the war when he his crushed by his horse at Belmont battle and William Tecumseh Sherman becomes the only high raking officer of the war to commit suicide.
Comment: IOTL Sherman suffered in that period of melancholia, todays known as depression. ITTL his depression is worse and one gloomy December morning he kisses his gun.
October 1861 - March 1862
The workers building the CSS Mississippi and CSS Louisiana are excused from military drills and the two units are fully operational by the end of March 1862.
April 1862
Farragut assaults New Orleans. While he is busy reducing St. Philip and Jackson, his wooden ships fleet is attack by the CSS Mississippi and CSS Louisiana. Union cannons do almost nothing to the Confederate ships while the Confederate point-blank fire mauls the Unions ships. The Unions fleet is de facto bottled by the river banks and escape is impossible. The battle ends in one of the worst naval defeats of history.
Comment: New Orleans remains under confederate control. A large port and the second most important industrial hub of the South significantly improves Confederacy commercial situation, blockade runners activity and industrial production w.r.t. OTL. Farragut ends up POW or killed.
February - July 1862
McClernand, being a much less inspired leader than what he thinks, does repeatedly makes a mess in the west.
June - July 1862
The Peninsular Campaign ends with Union retreat.
August 1862
After many very public disagreements with Lincoln, McClernand and McClellan are almost simultaneously relieved from command, leaving Union public opinion disconcerted.
McClellan beings a press campaign to warn the Union public opinion about the dangerously naive meddlings of the "Illinois amateur" in the conduction of the war. McClernand, fearing that his political career might be stunted by his uninspiring war performance, joins McClellan in the denigration campaign against Lincoln and his administration.
Comment: from now on, the "Two Macs" (as they are known ITTL), become the darlings of Copperhead newspapers and public opinion. Since they have been high ranking Union officers, Seward cannot just lock them up as confederate collaborationists.
August 1862
Second Bull Runs ends in a bloody stalemate. Union situation is not significantly better than ITTL but Lee has to put on hold his invasion plans while he rebuilds the NVA.
Comment: Pope remains for a while in command. The time shift in command changes will have a severe impact 11 month in the future at Gettysburg. B.t.w. this POD is an example that sometimes the way to wank Confederates is to make them lose
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November 1862
Mid term Union elections. The northern public opinion is especially affected by a map drawn by McClellan and published on Copperhead papers, map that shows that a year and a half of war have almost left the front lines unchanged. People begin overtly questioning the wisdom to continue "Mr. Lincoln's war".
The republican/federalist electoral cartel barely manages to remain in control of the House. The Union gives, home and abroad, the impression of mismanagement and division.
Without any clear victory, the Declaration of Emancipation is still sitting inside Lincoln's desk. Abolitionists are getting more and more disillusioned with the war.
February - April 1863
Great Britain, France and Russia offer to broker a peace between the Union and the Confederacy. Southerners immediately accept, northerners are divided between "Peace Now" Copperheads and "War until Victory" hardliners. Lincoln tries to put a square peg in a round hole but has to throw the towel and the war partisans win.
Some of the decidedly un-diplomatic comments of Seward have been "leaked" to the Union press and end on Palmerston desk leaving him and the rest of the british government decidedly unimpressed.
Britain ad France recognize the Confederacy. The Confederacy gets greater access to supplies, while Union buys are restricted. Britain and France governments looks elsewhere while british and french held shipyards around the world build commerce raiders for the Confederacy.
June 1863
Seward presses for the Union to declare war on Britain and France and invade Canada. Lincoln pithly comments "We are not managing to subdue the rebels and you propose to add two empires the list of our enemies?". Even Seward has to admit that the plan is not smart.
July 1863
Hooker almost manages to lose the battle Gettysburg. Only AoP numerical superiority carries the day. Lincoln declares anyway Gettysburg a victory and announces the Declaration of Emancipation. It is easy for the Two Macs to spin the Declaration into nothing but a cynic attempt to raise servile insurrection within the South.
The Draft Riots rock the North, from New York to Chicago. The situation is so critical that even Lincoln seriously considers Seward proposal to enact Martial Law in the whole Union territory. Lincoln administration popular approval reaches an all time low. Copperhead newspapers openly discuss the need for some kind of "action".
July 1863 - March 1864
Confederate raiders wipe out Union commercial fleet, inflicting a de-facto counter-blockade. The immigration in the North collapses, which, together with men dying/wounded/recruited creates a job market crisis which causes wages to raise. Market disturbances morph into the first signs of a severe inflation.
February 1863 - April 1864
Generals Thomas and Sheridan manage to hammer their way along the Mississippi.
The advance is not without side-effects since the confederates, highly outnumbered, switch to hit-and-run attacks, guerilla raids and piracy on the river. The Union has to employ a staggering amount of troops to physically control every mile of the river and of its banks. The resources required are so large that the Tennessee front has to be put on hold.
October 1863 - May 1864
Meade (nominated after Gettysburg) attacks several times Lee but he never bests him enough to begin a serious drive towards Richmond. The losses incurred by the AotP (e.g. in the First and Second Battle of Wilderness) are so high that newspapers start to call Meade "George the Butcher". Lincoln, feeling that now the Union appears to have found generals capable of fighting, publicly confirms his support for Meade. Administration public support, which had slightly improved after western victories, sinks again.
January 1864
The Two Macs and Pendleton begin their bid for the presidency. The democratic platform is that the war is totally mismanaged, the economy is falling to pieces and that Lincoln is risking every day the overt military intervention of Britain and France.
June - July 1864
New Orleans falls to the Union. The Father of the Waters runs again unvexed to the sea. The amount of troops required to keep the river under control precludes further operations on the west; Lincoln has no alternative but to bet the result of November elections on the Virginia front.
Comment: counter intuitively, the fall of New Orleans does not help Lincoln re-election bid: now that the Middle West is no more land locked, war support there wanes.
June - October 1864
Meade makes a supreme effort against Lee. A series of never before so bloody battles brings AotP near Richmond (a cavalry raid by General Killpatrick manages to reach Richmond outskirts before being turned back by General Forrest cavalry counter attack). The confederate switch to extensive field fortifications and to a completely defensive posture stops the Union tide at the 11th hour.
November 1864
The democrats win the elections. McClellan is President, Pendleton Vice President, McClernand Secretary of State.
Lincoln orders the cease fire along all fronts, Davis follows within days.
January 1865
Peace talks begin in Havana with under the aegis of Britain, France and Russia.
April 1865
The treaty of Havana is signed. The Confederacy accepts the situation on the ground (i.e. Texas being split away) and renounces to any further claim on CONUS territories; in exchange the Union accepts the Confederacy existence and agrees for toll-free transfers overland thru the Mississippi corridor.
Many people, north and south of the border, make no mystery that this is not a peace but just an armistice to prepare for Round 2.
As you can see, no AK-47s are involved, just the death of two very crucial persons, the timely completion of two ships and the confederates doing, by sheer luck, a bit less mistakes. I don't see this sequence of events terribly unlikely.