How about this?
POD 1915: US Vice President Thomas Marshall has a serious heart attack. Though he survives, the VP's flagging health coupled with Wilson's own health problems leads to many pushing for Wilson to replace the dull Marshall in the coming election.
However attempts to replace Marshall run into problems as the divides within the Democratic party begin to show leading to an impasse. Though starting as a joke, Thomas Edison's name is brought up and he quickly gains traction as a compromise candidate. When approached, Edison is initially hesitant, however for the sake of the scenario he is won over and agrees to run alongside Wilson in 1916.
Though close, the combined Edison/Wilson ticket wins with a slightly higher share of the popular vote (no Electoral College shift) than OTL. Edison quickly becomes disillusioned with the office of VP as, like his predecessor, Wilson cuts him out of the decision making process immediately.
This all changes in October 1919 when Woodrow Wilson suffers his final and most severe stroke. In OTL it left him incapacitated for months, but in TTL it kills him, making his VP Thomas Alva Edison POTUS. Edison immediately pursues a markedly different course of action than his predecessor. Any notion of America joining the League of Nations is dropped due to Edison's pacifist and isolationist views, and every effort is made to adjust domestic policies to "Return to Normalcy" in addition to promoting the implementation of technological changes.