For the next three years, the North was fighting to put an end to the institution of slavery and to bring the rebel states back into the fold.
No it wasn't. The EP was strictly a war measure. Lincoln went miles out of his way to ensure that it freed not a single slave. He even went so far as to make clear that this did not free any slaves either in the slave states which remained in the Union or in Confederate territory that was then occupied by Union forces.
Let's not forget that the South initiated the secession because of the fear that President Lincoln and the North would abolish slavery in the first place.
Let's not forget that this is false. Of the original 7 seceding states, only 4 issued declarations of causes. Of those, 3 listed reasons other than the Northern states' refusal to enforce the fugitive slave clause of the US Constitution which was actually unconstitutional and which did provide the seceding states with a sound legal argument that it was the Northern states which had violated the compact between them. Those reasons given were overwhelmingly the economic exploitation of the Southern states by the Northern states via partisan sectional legislation.
The 5, arguably 6, states of the Upper South did not secede until Lincoln chose to start a war to impose a government upon the seceding states which they did not consent to. They obviously were not seceding over slavery.
Lest anybody be confused, the Northern dominated Congress passed a resolution explicitly stating that they were not fighting over slavery. The Northern dominated Congress also passed and the president signed and several states ratified and Lincoln endorsed in his inaugural address, the Corwin Amendment which would have expressly protected slavery by constitutional amendment effectively forever. The original 7 seceding states rejected this express protection of slavery forever. Enough with the false propaganda that either secession or the war were "about" slavery.
Trying to quote Bruce Catton from memory: “The Union and the Confederacy disagreed about a lot of things, but one thing they did agree on was that, whatever the civil war was about, it was not about slavery.
“Except, of course, it was.”
(From The Coming Fury, if I’m remembering it correctly.)
The original seceding states did try to leave the union specifically to try to preserve slavery. With the free states dominating the House of Representatives, and gaining a majority in the Senate, they viewed the election of an abolitionist president as one crack too many in the wall, and felt the slavery within the United States was doomed.
One legislator, arguing against secession in Georgia (if I’m remembering it right) did say something like “Let us not break the constitution because, forsooth, he may.” This view did not prevail; Georgia was not going to wait for an unconstitutional action by the new president. They figured that the writing was on the wall. To preserve slavery, they needed to leave. Everyone tried to talk about other issues at the beginning of the war, but I don’t know that anyone was actually fooled by them. It is true that, once the “gulf squadron” enacted their bills of secession, that added another issue to the table. Once secession was attempted, the question of state versus federal power became a live issue. You can fairly say that the second wave of secession was launched by states which wanted to preserve their own freedom to leave if they wanted to later on. It was not a coincidence that they were all slave states, though. They were mainly concerned with having the right to leave, in case anti-slavery laws became too onerous. No free state even considered leaving to preserve state independence, and not all slave states did.
In the real world, the free states actually were enforcing the fugitive slave laws, and the clause of the constitution that allowed one state to extradite from another. That’s why escaped slaves did not stop when they reached a free state. They kept going to Canada or Mexico, which would not generally extradite escaped slaves.
Many people in the free states were sympathetic to the escaped slaves, and looked the other way as they passed. That reduced the ability of law enforcement to recapture the slaves. Every law is less effective among people who are opposed to that law; this was not a valid ground for breaking the constitution.
By the way, Lincoln did not choose to start a war. The civil war started when South Carolina enacted her ordinance of secession, just as an invasion starts when the first soldier steps across the border. In both cases, the fighting may come later, but as soon as someone tries to slice off part of a sovereign power’s territory by force, that’s war. Under the constitution, both the states and the federal government are sovereign. For a state to try to remove part of the territory of the United States from United States law, is war. It would also be war if the United States tried to remove part of a state’s territory from the state’s law. (With the overreach of federal power since the Roosevelt days, an argument can be made that we are already there, but that’s another topic.)