Thanks for the kind words -- wish I could help more. Since your information says Taylor was with the 6th Tennessee for a very short time, it makes sense that there may be no record for him with that command. I don't see a staff record for a William Taylor in the QM Dept., but he could have been detailed, which wouldn't change his original assignment.
In either case, I still don't see anything that fits.
Without looking at individual records -- and there are so many William Taylors -- we will not know for sure, and maybe not then. If he lived until the 1890s or later, perhaps there is a pension application or a questionnaire in his name.