It seems pretty certain that Thomas Donaldson's remains would have been moved to some national cemetery as unidentified. Rather than try to find him by researching the Army reburial records (which can be researched but not easily) find others who died in the same place and see where they are buried. I did a little looking and found one but there is no record of him either.
I was able to positively identify five other regiments on the Yazoo Pass expedition so you have a pretty good pool to work on.
43rd, 46th, and 47th Indiana and the 29th and 36th Iowa