Don,
I wish you luck in your search. Guess you don't have the names of the parents of Michael Rourke. Was it only the census that claimed Michael Rourke was born in Ireland? His death cert. would be alot of help, by 1936 the records should be well kept & informative. Was your grandmother alive when Michael died? Did he die in Worcester? An obit would be nice, that can be retrieved once the date of death is known.
I know of some Rourkes and O'Rourkes in Worcester prior to 1861, even if your Michael was not born in Worcester, he could be related. If you put a lot of stock in nameing patterns, I should mention that none of the first names you listed appear in Worcester in the mid-19th century (I know of about nine Rourke/O'Rourkes living here then.)