Placing "Packet Ship" as far back as the 18th C., or even 1855, is conjecture. Hugill's source was a bilingual collection of Danish shanties by a certain Capt. Jensen published in 1923, and it isn't clear whether the song was originally in Danish or English.

Nordhoff & Hall's novel "Mutiny on the Bounty" wasn't published till 1932, but the Mutiny was famous long vefore that. R. M. Ballantyne wrote a novel about it called "The Lonely Island" in 1880 and conceivably the shanty was based on that.

I don't know of any mention of "Packet Ship" independent of Jensen and Hugill.

Hugill thought the words must be old because they state that the crew had never been found. But that doesn't prove anything. Maybe Jensen's text was faulty, or maybe the shantyman just wanted to end his song.

There's no real evidence to show that "Packet Ship" was sung in the 1850's.