There wasn't really any reason to toss the Republicans out in 1928, but another splinter in the party amongst Old Right/Progressive lines could have certainly brought a Democrat win. Hoover, the great philanthropist, was ultimately a concession (despite his rugged individualist beliefs) after the doctrinaire Coolidge and corrupt Harding administrations, to the Progressives. If you have someone from the old Nelson Aldrich wing of the party nominated after a backroom meeting, you might get Dawes or Curtis or some other Midwestern Reformer type to run independently and take the Farmer vote with them.