The Declaration's one and only purpose was articulating a right to independence, which is what the Southern states were trying to have.
Making the Declaration into a statement on slavery is just wrong.
Lincoln was fighting against the purpose of the Declaration, not in harmony with it. Had Lincoln been truly respectful of what "our fathers brought forth on this continent.." he would have ended the war against those seeking independence from a government they saw as no longer serving their interests.
"I would save the Union. I would save it the shortest way under the Constitution. The sooner the national authority can be restored; the nearer the Union will be "the Union as it was." If there be those who would not save the Union, unless they could at the same time save slavery, I do not agree with them. If there be those who would not save the Union unless they could at the same time destroy slavery, I do not agree with them. My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery. If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it; and if I could save it by freeing some and leaving others alone I would also do that. What I do about slavery, and the colored race, I do because I believe it helps to save the Union; and what I forbear, I forbear because I do not believe it would help to save the Union. I shall do less whenever I shall believe what I am doing hurts the cause, and I shall do more whenever I shall believe doing more will help the cause. I shall try to correct errors when shown to be errors; and I shall adopt new views so fast as they shall appear to be true views." [Lincoln, Abraham, "Letter to Horace Greeley." Abraham Lincoln Online, 1858]
In fact, Lincoln was a white supremacist who was in favor of returning all blacks to Africa (as did Thomas Jefferson, and others):
"Colonization was hardly a fringe movement. 'Almost every respectable man,' as Frederick Douglass observed, supported it. Thomas Jefferson and Henry Clay, the statesmen most revered by Lincoln, favored colonization. Jefferson remained committed to the idea to his dying day. In 1824, he proposed that the federal government purchase and deport 'the increase of each year' (that is, children) so that the slave population would age and eventually disappear. Critics, Jefferson admitted, might object on humanitarian grounds to 'the separation of infants from their mothers.' But this, he insisted, would be 'straining at a gnat.'" [Eric Foner, "The Fiery Trial: Abraham Lincoln and American Slavery." W. W. Norton & Company, 2011, Chap 1, Part II]
"From the American Revolution to about 1820, surprising numbers of slaves were liberated even in the United States South as well as North. Yet one of the truly distinctive features of North American slavery, except for that brief period, was the virtual lack of hope for any change in status. This closing of doors and escape hatches resulted partly from the spectacular long-term increase in the value of slaves, which reflected a growing demand and limited supply. The restrictions on manumission also reflected the mounting pressures of white racismthe conviction, shared by virtually every national leader from Jefferson to Lincoln, that whites and blacks could never permanently coexist as free and equal citizens." [David Brion Davis, "Challenging the Boundaries of Slavery." Harvard University Press, 2006, pp.30-31]
This is from a short article on the subject:
""Founded by the American Colonization Society, a group of men who believed that freed slaves had better chances closer to their roots, Liberia became a beacon for the freed slave. Presidents of the Colonization Society included James Madison and Henry Clay. 'There is a moral fitness in the idea,' said the latter, 'of returning Africa her children, whose ancestors have been torn from her by the ruthless hand of fraud and violence.'" [Shirley & Shirley, "Revisiting the founding of Liberia." Washington Times, Sept 27, 2018]
That said, the Gettysburg Address was a political strategy in the midst of an unfavorable war: nothing else. If it was about slavery, Lincoln, using his usurped dictatorial powers, would have freed the Northern slaves earlier that year with his "Emancipation Proclamation."
Mr. Kalamata