Ah, true. However, I don't really see this is as a problem.
Kamihime is a multiplayer game. Communication is key. Simply talk to your Union mates about you wanting to turtle something, befriend them, get them to show up in your list... and there, you're ready to go.
For the... self-sufficient players, you can always make an alt account just for these Eidolons. This is against Nutaku's ToS however, so I wouldn't recommend it.