Stuart --
Look at the matter as former officers and men of Wheat's Battalion might have in 1865. It didn't really matter where they resided at the time. As bona fide participants in the 'rebellion', all Confederate soldiers had to have a parole to preclude arbitrary arrest and detention. Otherwise, all they had was a discharge paper issued by a government that Federal authorities didn't recognize.
If you had been a member of this command, wouldn't you have taken steps to get a parole? When asked the name of your command, what would you have written?