Those blankets are quite heavy, so I'm thinking what I'll do is to nail up 1"x3" headers all around the room. Then place hooks strategically around the boards to match the grommets in the blankets. Before hanging the blankets, paint the boards and hooks to match the room so they blend away should you need the room for something else later. Then hang the blankets.

I dunno...that's what I'm thinking of doing. Another thought is cableing all around the room, but that seems kind of chessy to me.