It is doubtful that either of these two collections would contain information on events occurring June 27, 1864.
You would either have to visit the Army Military History Institute at Carlisle Barracks, Pa to view these documents or have them copied for you.
U.S. Army Military History Institute
Collections Division
950 Soldiers Drive
Carlisle Barracks, PA 17013-5021
44th Illinois Infantry Regiment
The following pertinent personal papers are in the Institute's Manuscript Archive:
Bartholomew, Arthur C. (Pvt's letters, Sep 19, 1861 + undated)
Nichols, William G. – CWMiscColl-Hess Coll (Pvt's letters, Dec 31, 1861-Jun 5, 1864)