Nope your wrong there, not a professional....
still looking for my own family in Louisiana.

My guess is since I could not find any others they moved on and died or died in New Orleans before 1870.
The Civil War 1864 was going on and I didn't come across any recognizable Nash in it? Union or Confederate.
Nash Sr. (bn.1818) would have been old enough to join CW, & his son Zach Jr. 1847.
I wonder when/what age the boys were enrolled in the school?
That might indicate parents were dead etc.
And if there are any records in Baton Rouge Archives or New Orleans Library, and what happen to the boys after, were they apprenticed to some shoe maker? Surely New Orleans could not support all the shoe makers they were training. So they had to go where work was. How are you related and which child are you following, did the girls marry?
Questions - questions - questions