Dean this may be a lead for you, in my index of the Journal of the Congress of C. S. A. there was two Henderson one was James Henderson he was a Captain so it couldn't be him the other was J. C. Henderson and he was a Asst. Surgeon give no State. This is the only Henderson that the first name started with a ( J. ) I think this is him. The Journal had no more info on him.
I then went to the site of Soldier and Sailor System, and looked for him there. The only James C. Henderson from 2nd. Missouri was a Private. Then I tryed J. C. Henderson and this is what I found I believe this is him.

J. C. Henderson (First_Last)
Regiment Name General and Staff Officers, Corps, Division and Brigade Staffs, Non-com. Staffs and Bands, Enlisted Men, Staff Departments, C.S.A.

Went in as a Surgeon and out as a Surgeon
Good Luck.