The correct response to the Irish greeting, "Top of the morning to you," is "and the rest of the day to yourself."

Oh begorrah, warms me bhod, but that's another story.

Anyway, do such cod phrases (also like "Bless all in this house!") have any factual basis in Irish (outside of something like John Millington Synge's evident Anglo-Irish racisms?)

"Bless all in this house!" is very Irish.
I've read it in Irish language novels numerous times.

For examples (my translations) --

"Go mbeannaí Dia sa teach" (O'Dónaill's dictionary) (May God bless all those in the house)

"Go mbeannaigh Dia anseo isteach" (Seanfhocal na Mumhan 1926) May God bless all here inside the house.

"Top of the morning to you" is probably a misunderstanding of
"Mór agat ar maidin", which is common enough. Not clear whether the Goddess Mór (as in Dún Móire in Dún Chaoin) is meant,or whether, as Tomás Ó Maille in an Béal Beo thinks, it is borrowed from "Good morrow"

"God bless all here" was what I heard when Irish-born visitors arrived at my parents' door.