The piece was lost long before the war was won, and I doubt Lincoln nor anyone else could have done that.  As Union armies occupied Rebel territory, it became apparent the antebellum elite would be left in place.  It had to find its own way to stay in power, but the Union wasn't going to force them out, carpetbagger and scallawag fairytails by Moonlight and Magnolias morons notwithstanding.  The Union had neither the strategy nor the will to do anything beyond reuniting the country and ending slavery.  Stevens and the Radical Republicans were able to push their agenda for awhile, but it never took root, not in the target states of the South (of course), and not even in the Republican Party, which wrote off the South and the freed slaves the minute it was certain the Midwest could deliver elections regardless.