Your challenge, should you choose to accept it, is to come up with the least bloody way for the Union to with the American Civil War. Least bloody includes total military casualties on both sides.
There are a couple of important caveats:
ITYM "conditions"; a caveat is a warning.
(i) the PoD must be after 20 May 1861, i.e. after North Carolina votes to secede from the Union.
(ii) the Union victory must still result in the abolition of slavery within a reasonable timeframe after the war's end (say maximum of 8-10 years).
That's tricky. A quick Union victory, before the Emancipation Proclamation, makes abolition much harder. OTL's postwar shows that Southerners could be very ingenious in defense of their positions when given any opportunity.
It doesn't necessarily require much emancipation directly in the war itself, but eventual abolition must be a consequence of the Union victory.
Eventual abolition is inevitable - but within 10 years is much harder.
As to the least bloody Union victory: the PoD is a decisive Union victory at Bull Run, with the Confederate Army of the Potomac routed, and several thousand rebels captured.
This humilition would deflate the secessionist bubble at the start. Kentucky would declare for the Union, and also probably the Civilized Tribes in Indian Territory. Most of the secessionists in Missouri would give up.
In the CSA, Unionists would press for the rescission of secession declarations. However, Lincoln, very determined to end the war, would pledge firmly that there would be no interference with slavery in any state that returned to the Union.
Tennessee, exposed to invasion, could be the first state to rescind secession. Virginia is weird - by the time of Bull Run, the "Union " government in western Virginia had formed, and declared the Richmond government illegitimate. But only the Richmond government can act for Virginia.
Still, if even one state gives in, and Lincoln pardons the rebels there, the rush for the exits could start.
But abolition later... It's very hard to see how it could happen. Is it enough to have gradual emancipation plans in place throughout the country? Even accomplishing
that within ten years would be hard. (I do believe though that once that state is reached, general emancipation would happen fairly quickly. I.e. some years after gradual emancipation was adopted, there would be a move to just go ahead and emancipate all the slaves.)
Post-EP, general emancipation is easier, but ending the war quickly is not. One could improve the Union's fortunes in battle. Bruce Catton suggested that if the commanders of the Union Left and Right Grand Divisions had changed places, Fredericksburg might have been a decisive Union victory. But the CSA isn't going to fold up from one defeat. Even if it is a thundering success, with Jackson killed, Lee captured, and the Army of Northern Virginia effectively wrecked - it will still take the Union at least a year to finish off the CSA.
(It's also my opinion that once the EP is issued, Union victory = general emancipation. While the EP didn't affect the Border states and the Union-occupied parts of the South, I don't see how 80% of the slaves can be freed without destroying the institution.)