Elihu Root was considered by TR; Root begged off in deference to his health. Taft, however, was waiting in the wings. If Taft is on the Supreme Court, I suspect TR could have persuaded Root to accept; Root, on his part, would have extracted a concession: one term and one term only, with that proviso not to be made public in order to not impair the president's power.
With that, Root might not have romped home to victory in 1908--his association with Wall Street was pretty strong--but with the right running mate (e.g., the progressive Albert Beveridge of Indiana), he should have been able to take Bryan to school rather efficiently. And Root in the White House would have the ear of both Wall Street and the Progressives, given his ties to both.
Come late 1911 / early 1912, there's a meeting in the White House between President Root and former President Roosevelt. Root reminds TR of the bargain he made, and tells him he is about to announce that he will not seek re-election--on the basis of his health, to be sure. Moreover, he, Root, will endorse TR for another term.
That pretty much makes the 1912 GOP convention a celebration rather than a contest: the nomination belongs to TR in a walk. Philander Knox, an estimable conservative who is also acceptable to the progressive wing, becomes TR's running mate.
Meanwhile, the Democrats are busy hashing through ballot after ballot at their convention at Baltimore's Fifth Regimental Armory. Champ Clark makes a run but falls short; there's a brief boom for New York congressman August Belmont that goes nowhere. Finally, after 45 ballots, Woodrow Wilson is the nominee on the 46th ballot. He chooses Thomas Marshall of Indiana as his running mate.
Wilson, on the face of it, appears progressive; the voters know, however, that TR is genuine. On election day 1912, it's just short of a Republican landslide, and TR is back in the White House.