Well, you can't really do anything with the stones. Just think of them as the rare items in other FFs. Later on you'll understand the importance of them, but you don't really use them in battle for anything. And as for that sleeping thing, I just have someone throw a stone at them.

I would suggest getting someone else to become a caster instead of waiting because Beowolf and Reis (whom I don't usually use) show up pretty late in the game. Or you could just change your fighting style and try without a summoner. Maybe you have someone who's somewhat proficient in the art of Black Magic?