But the fact is that an air called "The Unfortunate Rake" existed in Ireland as early as 1808.

It's hard to imagine that an air with that name, which rather resembles Joyce's tune ("My Jewel, My Joy") said to have been learned in Ireland in the 1790s, did *not* carry the words of the song later called "The Unfortunate Rake."

Whether any associated lyrics then contained the line about "St. James Hospital" is unknown.

It seems to be pretty well established that "St. James' Infirmary Blues" did not exist before the 1920s. That British (or even American) singers would (or could) have arbitrarily lifted the "St. James" name from an otherwise unrecorded ancestor of the "Blues" and retrofitted it independently to older songs defies (my) credulity.