As an amateur historian of limerick verse and its origins (and the origins of its current popular name) I stumbled across this thread and thoroughly enjoyed reading it. Yes indeed, Stephen Goranson has done some excellent research on this topic ... just to let you know that the earliest reference in print has moved to an earlier one now:

The Oxford & Cambridge Undergraduates Journal of Nov 20th 1879, which takes us a year earlier still:

https://www.google.co.uk/books/edition/_/Hh8PAQAAMAAJ?hl=en&gbpv=1&pg=PA110&dq=%22limerick+rhymes%22

If anyone finds anything more on the topic, I would be very grateful if you might email me on:

stride.environmental@virgin.net

Many thanks and best wishes,

Doug (UK)

https://books.google.co.uk/books?id=Hh8PAQAAMAAJ&pg=PA110&dq=%22limerick+rhymes%22&hl=en&sa=X&ved=2ahUKEwiNn66FydLsAhWmUxUIHbgNA1oQ6AEwAnoECAEQAg#v=onepage&q=%22limerick%20rhymes%22&f=false