If you're not Catholic, it may help to know the parishes are organized under dioceses and archdioceses. I would consider contacting the modern-day archdiocese for Ann in GA and also LA. The archdiocese of New Orleans, which had several convents and orphanages, can be contacted via this website: http://www.arch-no.org/contact
The Office of the Archives, Archdiocese of New Orleans, can be contacted via one of these methods:
Mail: 7887 Walmsley Ave., New Orleans, Louisiana 70125
T: (504) 861-6241
I've called before to ask about an historical context subject, and reached a knowledgeable woman. I think I'd try calling them first for tips. They know where all the records are stored, etc.
If you don't have luck with the Archdiocese of New Orleans, I'd try the archdiocese for the rest of LA and those for GA. One in GA is Atlanta, of course, and I think the other is Savannah...Baton Rouge is another in LA, but not sure if it covers the everything outside the Archdiocese of New Orleans...
:) I'll do a lil' checking around and let you know if I find anything else helpful.