This is getting really interesting! I also think the 'shamrock' refers to his being from Ireland. I've had a look on a number of sites relating to convict transportation & there are comprehensive shipping lists; I can't find a record of a ship named the Shamrock. Equally, there was a ship named the Ile de France, but it wasn't built until 1926!
The only other possibility, as far as I can see, is that the region of France from Paris to the coast (Le Havre, etc) is named Ile-de-France, so I suppose he could have been shipwrecked when almost back (presumably being taken back to England, rather than Ireland), if the ship was blown off course. It might explain the 'speedy reply'! Mind you, you could hardly call what is now the English Channel 'the ocean wide'.....
As I can't let go of anything once I've started, I shall keep searching around to see if I can find out anything else.
I had a look around for sites on Baring-Gould as well but there don't appear to be any with song collections.