ACW Question: Garfield given a Division?

According to Peter Cozzens ("This Terrible Sound"), James A. Garfield was offered command of a division of the Army of the Cumberland by William Rosecrans. Quoting Cozzens quoting Garfield via Smith ("Life and Letters of Garfield"):

"Garfield, I have now got a division ready for you, but I want to ask what you think of staying here with me and taking the place as my chief of staff. I am almost alone in regard to counsel and assistance in my plans, and I want a power concentrated here that can reach out through the entire army and give it unity and strength".

As Garfield recalled it, this request was worded in such a way that he could not refuse. But, on the one hand, Rosecrans' personality suggests that he wouldn't even mention the offer of a division if he weren't serious about it. On the other hand, embellishing one's own importance was par for the course during Civil War recollections. So:

Question #1: Can anybody confirm or deny whether Rosecrans seriously offered Garfield command of a division, rather than just his OTL spot as Chief of Staff?

Question #2: (In the event that Garfield was seriously offered a division) Which division would Garfield have gotten? The timing is given only as "Mid February, 1863", and I can't find the Army of the Cumberland's Order of Battle for then - all the sources I found skip right from Stone's River to Chickamauga, mentioning Tullahoma if I'm lucky.
 
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