This is another idea I've had for a LONG time. The Silmarillion is JRR Tolkien's history of Middle-earth essentially, told through the ancient Elvish mythology. One thing I noted was how important music was. The Music of the Ainur created Eä, the World That Is.

Music is also important in Pokémon. Mew has a specific jingle associated with it in its first movie appearance. Lugia's song brought him back from near-death. Oracion calmed the mighty Dialga and Palkia.

What if one could take the Ainur (angels or lesser gods) and the legendaries of pokémon and merge them into one? Eru, the One, could be Arceus. Ulmo, Vala (archangel) of the Sea could be Lugia. Melkor, He Who Arises in Might and the Middle-earth equivalent of Satan, could easily be Giratina, or perhaps Yveltal.

The problem is, a mere rewriting of the Silmarillion would be rather bland. The Silmarillion is told in a very overview, third person omniscient light. Perhaps a first person narrative would be more interesting? Other than that, I'm not sure where to start. Any suggestions?

Well, then just don't copy/paste Pokemon onto an old tale, lol. Just base it from it. For example, the main story doesn't have to be in that old tale's era. In first person, you'd need a main character, too.

It's possible to "rewrite" what mythology the legendaries are based from pretty darn easily. What ideas have you tried to work with? An all Pokemon only world? Human interaction? Any "other" creatures? Or just an all "gods" type thing like the Greek gods.

Humans exist. Pokémon will either be their own entity or replace the non-human races (Elves, Dwarves).

It was going to be a bit of a retelling. Some differences, but the same skeleton. Should I change that? Try to be more original, so to speak?

Oh, ok then. That works out in that case. Then it'll work out, me thinks.

I don't know the myth you're talking about, so I can't be of much help, but it would be nice to be more original about it. Changing the setting is one way. :)