Mississippi has a very active board, so my suggestion is to post there and ask them.
I bet they would be happy to assist you as the guys that read and post there are really
up on everything relating to the Civil War.
More than likely since he was Union, your uncle's remains were moved to a National Cemetery
around about 1867 after the war was over.
It is very possible he is laying in a marked grave down in Mississippi.
Good luck.