May I ask for clarification on a crucial point before I continue: Does your first paragraph say prior to 1860 (or the formation of the Confederate States of America), Americans were not Americans, or did not consider themselves so? Many did refer to their home states as their identity rather than the United States - but it was a bit of a 'family' idiom. To the rest of the world, Americans were Americans - not Virginians or New Yorkers.
I can't say Lincoln had much to do with the altering of the Constitution, which was handled by teams of Trumbull and Stevens. The Civil Rights Act of 1866 was to insure the 13th Amendment was not circumvented, and many other supplementary legislations had to be enacted so that former rebel states did not vote for the amendments to regain Union status only to do a sneak-around in their legislatures to circumvent the Constitution. This was amazingly successful for nearly 100 years while the Federal government looked the other way. Had Lincoln had a second term, judging by his notes and statements, these maneuvers would largely have been exposed for what they were and nipped. Instead, Andrew Johnson preferred to let the South go on its way, which appeared to be back to perdition for a large number of Southerners - black ones.
Oh, I see you've added a post. Well, I don't mind states breaking off from other states and reforming as new ones but what you suggest is indeed off the wall. I don't see the advantage of forming separatist enclaves rather than working through differences to a common goal. Very few have reason to complain in the US that they cannot be themselves as long as they do not violate the law. Nothing's perfect, of course, but it still works better than what you suggest.
As to removing others' ways of life - 1860-1865 - I just can't help but smile! Sometimes others' way of life involves removing liberty, political power, culture, etc from somebody else. Kind of goes against the 'old' Constitution's guarantees!