Hello Lee,
He certainly was a prolific chap, wasn't he? He is listed as GRANT on the passenger list of the Jolly Rambler, along with his uncle, his uncle's wife and their children. I'll have to look at the thing again, but another cousin of ours found the entry when she went to the Society of Genealogists in Sydney. I believe another person found this too but I'm not sure that she would want to be on this chat site, so I'll leave her name out. On the printout, it clearly states that his name was GRANT, Francis Primeiron. This was from the Battye Library in Western Australia, on the index of ships. I too thought he must have changed his name to Grant after he arrived, given his history with his uncle, William Harris - it seemed logical, however, not so.
I wrote away for Primeiron's cousin's (Mary Ann Harris) death certificate, hoping to find more information on his uncle, William Harris, but it did not shed any more light on the subject. Her mother's maiden name was not listed.
Anyway, the name, Grant, on docking in Sydney is a certainty.
Cheers,
Rose.