My great-grandmother's parents both had the surname "Bettencourt" but she and her brothers and sisters went by "Amarant(e)" in the USA. It made finding them in the Azores records very confusing but there is nothing standard about surnames in the Azores. It seems they just pick and chose as they please as long as they can find someone with that surname in the near past. My USA Amarants had a grandfather named Jose de Bettencourt e Amarante.
Your Jose may be a fit although the dates are a little off from the Jose I have in the Manoel Silveira da Bettencourt and maria de Sao Jose family. I have Jose Silveira Bettencourt b. 4 Feb 1809, Sao Jorges Azores m. Maria Eusebia 22 July 1839, Velas, Sao Jorges, Azores b. 8 June 1816, Velas, Sao Jorges, Azores. This information comes from a lady who is also related to this family. Since 9 and 6 are easily transpossed, my guess is that I may have entered the date wrong or just got turned around in the transporting from one person to that other. I have a baptismal record and marriage record for my Antonio but none of the other children. I also have baptismal and marriage records for the parents, Manoel and Maria.