I think you are way overestimating Rosecrans' chances. See Allan Peskin,
Garfield: A Biography. (Garfield was the chief booster of Rosecrans for vice-president at the Baltimore convention.)
"Garfield was certainly not blind to Rosecrans's erratic temperament, his vanity, his constant need of reassurance. Under the circumstances, his efforts in his behalf at Baltimore bear a touch of irresponsibility. It seems to have been a spur-of-the-moment effort, without advance preparation or consultation; an expression of Garfield's boredom with the convention and his desire to play the role of kingmaker. He dashed off a telegram to Rosecrans asking permission to enter his name in the vice-presidential contest. Rosecrans sent back a verbose but indecisive reply, as ambiguous as the famous order at Chickamauga and with similar effect. His friends at the convention retreated in confusion and the nomination went to Andrew Johnson, with whom Garfield had been in 'intimate acquaintance' ever since Johnson had been War Governor of Tennessee. Johnson was a friend of Garfield's and presumably radical, so that Garfield was content. He was not as well pleased with the main work of the convention. 'Of course we must all go for Lincoln if a Copperhead is the alternative,' he told a friend, 'but we have made a fearful mistake in nominating him.'"
https://books.google.com/books?id=SRmY164czTQC&pg=PA240
What about Stanton's alleged interception of the letter? This seems to be speculation on the part of Rosecrans, though accepted by his biographer Lamers (
The Edge of Glory) and the Wikipedia article on Rosecrans. However, as Peskin writes:
"34. Lamers, in
Edge of Glory, 424-25, maintains that Garfield never received Rosecrans's reply, presumably because Secretary of War Stanton used his control of the telegraph lines to suppress it, thereby dooming the Rosecrans movement. However, a copy of this telegram does exist in the Garfield Papers, LC, dated June 7, 1864, and bearing a comment on the back dated the following September. This clearly indicates that if Garfield did not receive Rosecrans's wire in June he must have seen it quite soon thereafter. Since he nowhere betrays any irritation at having his telegrams intercepted and, in fact, never indicated that there was any irregularity at all, it seems reasonable to assume that it was delivered on time and that Rosecrans lost the nomination on his own merits and not through the machinations of Stanton."
https://books.google.com/books?id=S...oks.google.com/books?id=SRmY164czTQC&pg=PA643
There really is no reason to think that Rosecrans would have gotten the nomination, even if his response to Garfield would have been less ambiguous. Not only was his role at Chickaumaga controversial at best but he was a Catholic in an era when the Catholic vote (compared to the twentieth century) was still small and the anti-Catholic vote large. The Know Nothing movement was only a decade in the past, and nativists remained powerful in the Republican/Union Party. Indeed, Fremont may have lost in 1856 partly because of false rumors that he was a Catholic.
https://www.alternatehistory.com/forum/threads/the-real-reason-fremont-lost-in-1856.444186/ And hostility by nativists was one reason Seward was defeated for the Republican nomination in 1860. Besides, Lincoln wanted a southerner to advance the cause of reunion--if he couldn't get Johnson, I think Joseph Holt of Kentucky would be the most likely choice.
https://www.alternatehistory.com/fo...t-lincoln-veeps-in-1864.444947/#post-17102564