Just my 2 cents ...
1. You might also want to send for the CIVIL Vital records for Mary Louise/Clara RAPP.
Check the Louisiana State Archives - they are very responsive and the cost is more than reasonable.
For New Orleans:
A CLARA Spriggs (50 years old) died 22 May 1929.
A Mary Louise Spriggs died (88 y/o) 19 Jun 1922.
Ernest and Ernestine Spriggs (Twins of Clara and James) were born 10 Oct 1873.
James Spriggs died 4 Apr 1883
There is ALSO a death record for a 48 year old Mary Louisa Spriggs, who died 20 Jun 1918. Not sure if she is related to your Spriggs/Rapps.
2. Sending to the archdiocese is most probably a good move. All church records prior to (about) 1925 (birth/christening, marriage, death) were sent to the respective (LA) Archdiocese. The Archdiocese of New Orleans covers seven or eight parishes around New Orleans, including Jefferson and St. Bernard (where there were early Rapps). The only down side is that those records are slightly more expensive than civil vital records.
3. Surname History (perhaps)
-a- There were German Rapps, and also Rapps that came to New Orleans from Santo Domingo and Cuba. Remember the uprising in the area beginning in the late 18th century sent many to the Gulf Coast and Cuba. Tens of thousands of families, including free people of color, came to New Orleans.
-b- In the early 1700's a German RAPP (Thomas) arrived in the area via ship.
-c- La Racounteur, a Genealogical periodical by LE COMITÈ DES ARCHIVES DE LA LOUISIANA, published the New Orleans Free People of Color Registers over several years! One lising mentioned slaveholder Laurence Ursule RAPP; the freed registrant was from Santo Domingo.
Another slaveholder mentioned was Peter RAPP.
Due to copyright, I refrain from posting the entire contents. I can send the details. Contact the Genealogical society at the following link.
-d- There are RAPP free people of color in and around Orleans Parish as early as 1832, when Antoinette, Marie, and Celestine RAPP appear as parents in New Orleans vitals. Antoinette married a MATHIEU (from Cuba?). Marie married Joseph Fouche. Celestine married another free person of color - Boyer of Santo Domingo.
-e- Another connection is to the Fonverge / REY family. This is an old family of free people of color. Eugene RAPP (mulatto) married Philomene? Alphonsine REY. He is enumerated next to Arnaud and Henrietta Fonvergne in 1870.
No proof this is your family, however, the fpoc community was fairly close and intermarried in pre and post Civil War Louisiana. This possible connection is worth following. [Eugene was a Tailor.]
-f- Another clue was in the published (New Orleans) Archdiocese Records Vol 10.
RAP (alternate form = RAY). Could this be REY? [Just speculation, but since you have yet to find them before 1860, I'm listing POSSIBILITIES, not probabilities.]
Wishing you the best in your research.
¹ Riffel, Judy. LA RACONTEUR, "Register of Free Colored Persons (1840-1864)". LE COMITÈ DES ARCHIVES DE LA LOUISIANA XV (1995): 110-111.
² Sacremental Records of the Roman Catholic Church of the ARCHDIOCESE OF NEW ORLEANS. Vol 10 (1810-1812).
³ Ancestry.com. 1870 United States Federal Census [database on-line]. Provo, UT, USA: The Generations Network, Inc., 2003. Original data: 1870.