The source here I think would be a record NOT linked to the Andersonville camp. That's kind of the red herring in our search. If this unknown woman exists it sounds like she died in service, was buried somewhere in south Georgia or north Florida and was then reinterred at the cemetery that also holds the dead from Andersonville. I think using Andersonville in searches is pushing us towards stories about the camp, which likely don't concern this woman.
Good point. Okay, let's regroup.
If she "died a soldier," she probably died of sickness, but in battle is also a possibility. Were there any battles in Western Georgia on or shortly before April 4, 1864? Or possibly in Western Alabama? I think North Florida would be too far away from a reinterrment - it's over 100 miles away from Andersonville.
Found a Congressional document that lists the places that those reinterred were moved from: "Macon, in Bibb County; Columbus, Muscogee County; Americus, Sumter County; Louisville, Jefferson County; from the line of the Central Railroad; and in Alabama, Eufala, Barbour County. The greatest distance being 125 miles. Some 10 or 12 bodies are yet to be removed." Unfortunately, this account says that there were presently Thirteen thousand, seven hundred and five internments in the cemetery, so it looks like the Unknown Lady was the first of these "ten or twelve" to be buried. Even so, this gives us some idea of where to look, and she likely died within or just beyond a 125 mile radius of Andersonville. Here's the link, if anyone is curious.
She's listed at the top of the page, so I can't see who's buried just before her on the cemetery register, but the rest of the burials on her page are one unknown, but two of the others are listed as dying in August, 1864 and one died in just "1864." I can't make out the names of most of them, so I'll wait until I can get a clearer copy. One of them looks to be "Arthur Ford" who died in "1864."
I'll post more as I find more.