Do we really know that? We have only the word of "a scullery maid" on that. (Though I do wonder what his "last gig" was ...)

Mrs. Claus said Bun-Bun was present when the second egg was used, and I would expect her to be very familiar with the history of the eggs. I don't know when else Bun-Bun was around when magic eggs were used. And there was a Mohkadun story about the Rabbit God and the magic eggs ... (2nd-from-last frame)

Destined to be the Easter bunny, after all! Not a bad gig. Work really hard one night to earn his other 364 days of laziness.

She said the second egg was used when Claus was still young, so I'd say after the Greek gods were gone, if it's the best ballpark we can make...

How sure are we about the veracity of that story though?

Regarding Basphomy's time beginning, that doesn't necessarily have to correspond to her creation/birth or even a name change. Most likely it refers to her time as ruler of a holiday (which may or may not coincide with her taking the name Basphomy).

I don't think she ever ruled any holiday (though she was lured into ruling one by Pumpkinhead King and Bunbun). She is just an emissary of Dulunnoa.