Altough I am not an American, as an outsider I consider that the best electoral system for electing the President, taking into account the state's power in the federal system as well as the will of as many voters as possible is an Electoral College formed by electors atributted by proportional vote. This system also has the advantage of promoting third party candidates and thus allowing for the reform of a political system under the effective dictatorship of two parties, who, during the past 150 years changed ideologies back and forth and effectively became Big Tent.
So, your task, with a POD during the Progressive Era, is to allow for the adoption of the Electoral College and speak about the changes it would have on the history of the US. Double points for a presidential election example and triple points for an electoral map.