The thing is, he did just that in the West after Shiloh
Halleck didn't have any desire to take field command and would more then likely do what he could to prevent it. I am no expert by any means but I remember reading that after the Fredericksburg fiasco Burnside wanted to commit to an offensive and his generals didn't. Lincoln asked him to go down and speak with all the generals and make a decision. Hallack refused and even offered his resignation when Lincoln made a comment about his lack of desire to be on the field.
The thing is, he did just that in the West after Shiloh; assembled what had been Pope's, Grant's, and Buell's armies and marched (ever so cautiously, but still) on Iuka and Corinth. His forces managed to win both, as well (more or less).
One of the issues that 2nd Manassas raised was whether Halleck should have goine into the field and served as what would have amounted to an army group commander over Pope and McClellan; that - in a situation where McClellan and Pope have both been supplanted after 2nd Manassas and before Antietam - remains one of several options for high command in the east.
Halleck was brought east in 1862 to serve as general-in-chief, not chief of staff; one could expect Lincoln might have been insistent.
Given the above caveat, the "most likely" options include (in no particular order, and setting aside the question if Porter gets cashiered or not):
Burnside
Franklin
Halleck
Hooker
Mansfield
Sumner
Porter
Best,