Without going down the detail heavy rabbit-hole delay the Civil War a generation. Harrison is one of the few Post-War Republican Presidents who can reasonably be said to not have needed the war to "make" him, though it helped. Obviously delaying the ACW is a can of worms with massive butterflies and requiring complex developments but, have the decisive crisis occur some time in either the 1880s or 1890s with him as the alt-Republican trigger that starts the whole thing. And then have him have the courage and drive to pull off a Lincolnesque victory.
