Hang in AbstractHandleableCloseable.close() after remote EJB invocation in EAP 6

Issue

When clustered, we see all our apps deployed and running fine but within a random amount of time, we see EAP simply stall. A thread dump shows a hang at:

   java.lang.Thread.State: WAITING (on object monitor)
    at java.lang.Object.wait(Native Method)
    at java.lang.Object.wait(Object.java:503)
    at org.jboss.remoting3.spi.AbstractHandleableCloseable.close(AbstractHandleableCloseable.java:177)
    at org.jboss.ejb.client.remoting.EndpointPool.safeClose(EndpointPool.java:281)
    at org.jboss.ejb.client.remoting.EndpointPool.release(EndpointPool.java:101)
    at org.jboss.ejb.client.remoting.EndpointPool.access$400(EndpointPool.java:61)
    at org.jboss.ejb.client.remoting.EndpointPool$PooledEndpoint.close(EndpointPool.java:218)
    at org.jboss.ejb.client.remoting.RemotingEndpointManager.safeClose(RemotingEndpointManager.java:63)
    at org.jboss.ejb.client.remoting.ConfigBasedEJBClientContextSelector$ContextCloseListener.contextClosed(ConfigBasedEJBClientContextSelector.java:192)
    at org.jboss.ejb.client.EJBClientContext.close(EJBClientContext.java:1162)
    at org.jboss.ejb.client.naming.ejb.EjbNamingContext.close(EjbNamingContext.java:424)
        [...]