French merchant ships would have Swedish cast- iron guns with wrought-iron swivels until the first couple of decades of the 18th century, when they begin their own iron industry in earnest.
Oldest identified cannon are bronze, like the Loshult piece. First technology comes from bell and bronze...
There's a lot about La Rosa in the Royal Gazette of Jamaica July 1816 onwards; in the British Newspaper Archive Home | Search the archive | British Newspaper Archive. The location for the wreck it gives is Abaco.
The cannon was at Woolwich, not the gunfounder. However now, the guns have all left the old Rotunda collection- that one is either in Wiltshire or Fort Amherst in Kent. Of course at Woolwich there was only a brass foundry. Mathews went bankrupt at the American Wars as the government couldn't pay...
The gun with the Z was cast by George Mathews of Calcuts in Shropshire 1770s- 1780s. He supplied guns to the British government and the merchant market, including the East India Company. You might have the word SOLID on the other trunnion, or another Z and a number.
For 17th century material dendrochronology is a more reliable dating tool. The National Museum od Denmark dendro-ed the Anholt guns beds- always "said" to be 14th or 15th century, to discover they were c1520s. 93-10.pdf (natmus.dk)
you might be looking for the wrong home port. There was a Caledonia sailed from Glasgow in September 1795 for Jamaica. Glasgow had strong connections with the West Indies trade. the fact it is called Caledonia suggests a Scottish connection or origin.