Okay
You can look at the broadside yourself easily enough. The original is on the UCSB English Ballads website. I would say it could have been printed any time in the 18thc. On the opposite page with similar type is another sheet with no imprint about Paul Jones exploits in 1779.

It is a definite Cassilis version although it spells it Lady Castle an easy slip for an English broadside from oral tradition.

Ebsworth also prints the 1740 Ramsay version and gives 3 pages of historical detail on the event mentioned by Gutcher.

I'll now check the St Clair version with the SMM and Herd versions.