1) Think about stateful ejb. I think that it should work for you if you don't need to get this object from another clients.
2) I don't think that everything that works with static objects and thread is good in EJB. It won't work in a cluster. That's why I'm not sure that it's possible to share this object by reference with another threads.
3) May be JbossCache could help you to store/access some temporal results of this method execution.