I don't find any of your, or any other researcher's, efforts daft at all

Nor do I, I hasten to add - tracking down the bits of social history that have fed into the history of songs is always interesting & instructive. What I do think is daft is the assumption that every line in a song must have a real-world antecedent, so that if only we had good enough baptismal records we could find the real Henry Martin and the real Patrick Spens. I remember Dick Miles asking on here some time ago, Who put the parrot in the Outlandish Knight? We'll never know, any more than we'll know who gave the captain of the Dolphin a younger brother.

The mission of the Dolphin does seem a bit confused - to the point where it's not entirely clear that it's the French ship which is claiming to be a pirate. Which for me strengthens the impression that the song as we have it is a mutated version of a modified form of a variation on an earlier song - although there is an actual Dolphin somewhere in there!