Thanks to Big Lefty who caught me being carless....
The quote I used above is from the Tyler section of Dean's book (that's the problem with Parts 5 & 6 adding up to 1,200 pages!).
Okay, let me try to straighten my own mess up here.
1st (to the original question): There is no definate date that small arms ammunition production was begun..."On November 30, 1863, Major Rhett complained that cartridges were only being fabricated in the T.M.D. at the Shreveport Arsenal, but he would “soon have two additional Laboratories at work at Tyler & Marshall.” Interestingly, Tyler began production at the end of October in a rented facility, and we would think that Marshall was not that far behind."
Follow-up questions / comments: Houston's machinery went to Anderson;
Arkadelphia's machinery went to Marshall;
Little Rock's machinery travelled
through Arkadelphia to Tyler;
Shreveport made much of their own equipment but did get some stuff from New Iberia.