The problem for the Republican elites is that they have no obvious second candidate after Hanna. While Roosevelt hasn't alienated half the party like he had done in 1912. And since McKinley himself had always refused to be kingmaker, I think the Republican elites' only chance to stop Roosevelt is to convince McKinley to run for a 3rd term.
How much "stopping" would be required?
There were far fewer Direct Primary sates in 1904 than in 1912, so a primary campaign stands no chance. McKinley's successor will be picked in "smoke filled rooms", and by much the same men who buried TR in the Vice-Presidency to remove him from any position that really mattered
SoW Elihu Root or AG Philander Knox are obvious possibilities, but there would have been many others.