I think you're overplaying that "eliminating slavery also" stuff. But, you're entitled. You won the war, so you get to rewrite history. But, what did old Abe say himself?

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.


A. Lincoln, Letter to Horace Greeley, August 22, 1862.