It seemed to me that the amount of bullion was pretty light for New Orleans so I did some analysis. From 1858 - 1861 the Troy OZ production of the southern mints is as follows:
Numbers in .900 fine (coin alloy)
1858
New Orleans - silver 3,115,994 OZ
New Orleans - gold 48,643 OZ
Charlotte - gold 11,660 OZ
Dahlonega - gold 4,315 OZ
1859
New Orleans - silver 1,557,400 OZ
New Orleans - gold 11,019 OZ
Charlotte - gold 8,840 OZ
Dahlonega - gold 3,354 OZ
1860
New Orleans - silver 1,084,988 OZ
New Orleans - gold 13,061 OZ
Charlotte - gold 4,985 OZ
Dahlonega - gold 4,017 OZ
1861
New Orleans - silver 1,012,940 OZ
New Orleans - gold 19,071 OZ
Charlotte - gold 1,859 OZ
Dahlonega - gold 496 OZ (estimate, some sources say as high as 617 OZ)
Production for all southern mints dropped of considerably from 1858 to 1859. Also, New Orleans managed to produce essentially the same output in 1861 as in 1859 and 1860 even though it supposedly did not operate the entire year. I do not have a source for bullion purchases and shipments for these mints. Was bullion being stockpiled after 1858 or just less purchased and/or shipped? It seems Charlotte and Dahlonega may have had more unused gold bullion in 1861 based on the output drop. Also, I assume the mines in the area continued to produce throughout the war, but possibly not.