Hmm, I can see some combo possibilities for this... Diffusion Wave Motion (hope I remembered the card name correctly) would be very useful. You'd need something to dump monsters before it could attack at all, though. Maybe Painful Choice, or something...
Speaking of which, is it certain that the Exodia pieces must be dumped through Exodios' effect? I guess it would be broken if that wasn't the case (Painful Choice + Graceful Charity = win), but it's worth asking anyway.