The Early Settlers book has some errors in it, primarily because she did not have access to the full text of the records. One such mistake is in the Alfonso/Alphonso line. The father, Diego, of Juan Alfonso, is not the same as the one who came from the Canaries. Through sacramental records that provide a baby's grandpts' names, it is clear his father, Diego, was married to Angela Cazorla, of Tirajana, Gran Canaria. Page 54 of Gilbert C. Din's book, _The Canary_Islanders_of_Louisiana_, mentions this Diego when discussing how some Spanish soldiers and sailors from other provinces of Spain, including Cuba, married the recently arrived Canary Islander girls and remained in Louisiana. (Spain had two fixed regiments in New Orleans, many of whom were enlisted through a draft in Spain, and were thus not colonists or settlers.) She does include many research "clues" and she herself advise people to order copies for verification of what she's gathered. Still not many do, and so there are tons of people our there who incorrectly include the Canary Islander, Diego Alfonso, as our ancestor.
I recommend using worldcat.org to find a library near you with a set of the bound Sacramental Records for the Archdiocese of New Orleans, which cover 1772-1831 of St. Bernard's records. Sit down with them, record siblings' names, whom they married, etc. And read the introductory material in the beginning. It will tell what years and what types of records (baptisms, marriages, interments, etc.) are included, and for which churches/parishes. It will also introduce you to the many ways names can appear. Sometimes as if transformed into French names (Santiague, Jacques, Jean, Pierre, Rodrigue, Molere, Alphonse), and other times as if Spanish (Santiago, Santiago, Juan, Pedro, Rodriguez, Molero, Alfonso).
Re: establishing deaths, for example, or finding the origins of an ancestor in the late 1700s and early 1800s, you can narrow down some death timeframes by examining their children's on-going sacramental records. You may not find an interment for "Juan Doe", but you may find a year where one of their children married or had a child, and the "Juan Doe" is named as the bride or groom's parent, or as one of the baby's grandparents. Then later you may encounter a similar situation, but now "Juan Doe" is is listed as "Juan Doe, dec." Dec.= Deceased. Just remember to also look for records about children, grandchildren, siblings, etc. Priests often included places of origin in many records, but they might have not have recorded locations for some records. Yet you might find locations in other relatives' records!
One last tip, the 1860 Census was taken in the French and Spanish manner, meaning a married woman was listed by her maiden name. That's a great bonus for researching!