@PersistenceContext(unitName = "PrototypeCRMSystem-ejbPU") private EntityManager em;
Oddly, I got it working by luck and I'm still tracking down what I did. I tried your suggestion (unitName="...") and that didn't work. But I did get it working using a JNDI lookup rather than injection (see http://forum.hibernate.org/viewtopic.php?p=2402399#2402399 for more details).
As and when I find out what I did, I'll post back in case someone else sees this in the future