1) the person on the remote island is no catechumen yet you attempted to justify his salvation without the sacrament. This serves as an excellent example of how easily and how far from the truth BOD leads people.
How can a native on a remote island be a catechumen! The definition of a catechumen is "A non-baptized adult under instruction to be received into the Church"...
2) Prior to the 1917 Code of Canon Law, the Church taught that "neither the commemoration of Sacrifice or the service of chanting is to be employed for catechumens who have died without baptism". - Council of Braga 6th century
I'm shocked that you used the quote from the Council of Braga against baptism of desire, when the Catholic Encyclopedia, under the article on Baptism, references the same quote in favor of it! Full context below. The same quote is used in favor of Baptism of desire since a "commemoration of sacrifice" is not needed for catechumens, since they are assumed baptized by desire. The article gives an example of this with the Emperor being assumed to have baptism of desire.
Note, only one paragraph after this one, in the same article on Baptism, there is the section called "Substitutes for the Sacrament" where it goes into all the proofs for baptism of desire and baptism of blood. Better scratch the quote from the Council of Braga from your arsenal!
Catholic Encyclopedia, Baptism
"A certain statement in the funeral oration of St. Ambrose over the Emperor Valentinian II has been brought forward as a proof that the Church offered sacrifices and prayers for catechumens who died before baptism. There is not a vestige of such a custom to be found anywhere. St. Ambrose may have done so for the soul of the catechumen Valentinian, but this would be a solitary instance, and it was done apparently because he believed that the emperor had had the baptism of desire. The practice of the Church is more correctly shown in the canon (xvii) of the Second Council of Braga: "
Neither the commemoration of Sacrifice [oblationis] nor the service of chanting [psallendi] is to be employed for catechumens who have died without the redemption of baptism."