The First World idea is definitely a great one. After all, if the laws of reality there are bendable, and nothing is truly set beyond what the most powerful creatures dictate, it would make a certain amount of sense that people could tap into these prototypes and shape them to their own will.
A couple other possibilities occur to me:
1. Eidolons are natives of the Dimension of Dreams, whose form change on a regular basis as they're caught up in the night time excursions of mortals. A summoner could tap into one of these spirits in a dream and bring the figment across to the material plane.
2. For a more sinister twist, Eidolons are bound Moonbeasts from Leng. Described by H.P. Lovecraft in The Dream-Quest of Unknown Kadath, "Great greyish-white slippery things which could expand and contract at will, and whose principal shape — though it often changed — was that of a sort of toad without any eyes, but with a curious vibrating mass of short pink tentacles on the end of its blunt, vague snout.” Notice the bit about how they can expand and contract at will, and how their principal shapes often changed. In fact, I might stat up a Man from Leng with a Moonbeast Eidolon.