ManagedExecutorService is exactly what you want to use for this.
The availability of this service in JEE is a great benefit. In the past, we basically just ignored the guidelines and managed all of this stuff ourselves.
The MES allows you to capture the context information of the invoking component, and tie your task in to the life cycle of the container. These are both very important in the JEE environment.
As to where to start the task, you basically have two options.
One, you can use a ServletContextListener, and have that kick off the task during container startup.
Two, you can use an @Singleton EJB, and tie in to its lifecycle methods to start your task.
If you start the task up from the ServletContextListener, then the task will run as if it's in the WAR environment. If you start it up from the @Singleton, it will run within the Session Beans environment (this mostly relates to how the JNDI appears).
Either way, you only need to worry about starting the task via these mechanisms. You should rely on the ManagedTaskListener.taskAborted interface method to shut your task down.
In theory you can work with the Thread.interrupt that is sent to your task during shut down. I've never had good luck with that myself, I rely on an external mechanism to tell the long running tasks to shut off.
I wish I could give first hand experience with this new facility, but I haven't had an opportunity to try it out yet. But from the spec, this is what you want to do.