Tom,
I think that the book This Republic of Suffering by Drew Gilpin Faust addresses many of your questions, particularly in Chapter 7: Accounting. Congress passed legislation in 1867 for national cemeteries for Union dead, although some private efforts and some by the U.S. Army had already begun before then. Efforts were headed by the Quartermaster Corps first relied upon friends and family reporting what they knew to the government, then bounties were offered.

George