So... the other day I turned in two red chococards to Finbarr for a honeymoon and then started the Chocobo on the Loose quest with Brutus... and the chocobo that wanted out was red (previously on other characters I'd only ever seen yellow)! To test it, I ran a new character to Jeuno (at great personal risk) with two blue chococards, turned them in, and the chocobo that wanted out when I started the quest with Brutus was... BLUE.

Is it possibly that while Finbarr is cooking up your special honeymoon egg that it affects the genetics of the quested egg?

Sadly, since you have to be level 20 to get the quested egg back I will be too impatient to not pick up my honeymoon egg on the new character.