Thanks to all who commented~

"Egan's Favorite" is indeed "The Stack of Rye." (Now that I know it, I prefer Crehan's title):


https://www.youtube.com/watch?v=Dq-lB6gquu8


And the Corrs' jig might well be "The Rakes of Kildare" or it might be just different enough to have another title. Or it may just be their version of it.

I agree it's not quite the usual form. I used to play "the "Rakes,"" but this time I couldn't recognize it !

Usually sounds like this:

https://www.youtube.com/watch?v=yU8A3TdBEb8

When "The Limerick Rake" is played as a jig, it sounds a lot like "The Rakes of Kildare." I believe Natalie MacMaster recorded it long ago, I think without a title.