I confess: I can't give up. Trying every way I can to find any sign of the right John Kelly back in Ireland, I've backtracked to some original sources. In an old-fashioned way: microfilm.
Not that I've really resigned myself to cranking through records on a microfilm record. This attempt is the next "best" thing. (Admittedly, nothing is "best" about having to read handwritten records on a microfilm reader.)
I've gone back—virtually, of course—to the National Library of Ireland, where lo and behold, there are some microfilmed records for earlier years of some of the locations in County Kerry where I first spotted John Kelly and his wife, Johanna Falvey. Keep in mind that the dates I've retrieved for John's birth vary wildly. Some of those dates reached beyond those available in a crisper, cleaner digitized form at either Ancestry.com or FamilySearch.org. Believe me, these older records show their age.
Thus, I now enter the stage of a "reasonably" exhaustive search. While I'm not sure it can be considered reasonable, I'll be reading through the birth entries, page by page, starting with the early 1800s in the parish of Killeentierna.
Though the copy is fuzzy, it is still fairly easy to differentiate "Kelly" from all the other blurry surnames, so progress won't be too agonizing. Much time to search means little time to write about it, though, but if I find something significant, I'll come up for air long enough to tell about it.