If anyone else has a better understanding of Japanese folklore they should speak up, but it sounds to me like Kokutandouji is meant to be a play on Momotaro. Particularly considering how he goes to a place called Onigashima.
I'm also hesitant to try and pin down any readings for names that the website hasn't given us. The Envy novel will most assuredly have them and pronunciations of kanji can vary wildly between names. Me personally for example I assumed the man's name was "Kuroo" or "Kurotoshi", not "Kokuo" and "Kurookina", because the pronunciation of those in name usage is different than in word usage.