Banging Rico's head against the internet

Rico says he keeps looking on-line for a story that he knows (because he has, somewhere, a copy of it) was printed in Playboy back in the Sixties, entitled The Ballad of the 656th (or something similar; he's now gonna have to find that hardcopy to make sure), about a unit that gets transitioned (hey, it's science fiction, everything works), due to being in the blast zone of an unannounced nuclear bomb test in the piney woods of North Carolina in 1965, back in time to the same place in 1865.
Now, you can imagine the resulting difficulties, especially for an Army unit of mixed (meaning North and South, not color) soldiers, armed with 1965-era weapons...
Great stuff, whether you like Civil War, science fiction, or (like Rico) both. Rico says he wants to republish it in his Civil War magazine, but first he's gotta find it...