Okay, I finally got it figured out. There were two missing pieces when I originally posted this 2 days ago.
One, I didn't know I needed to package my bean classes in a separate jar and declare it in my application.xml. So thanks to Wolf-Dieter for that bit of information.
Two, when attempting to access the bean from my code, I was using InitialContext.lookup() and supplying a string of "<ear-name>/<bean-name>/local". I didn't realize that I had to supply the full ear file name, including the version. That seems a bit klunky to me, to hard-code a version ID in my Java code. But once I got past the first hurdle of declaring my EJB jar file in the application XML, I was able to see the name JBoss was using to bind my bean to JNDI, and I saw that indeed the version ID was there.
So once I specified the JNDI name correctly, everything worked. Thanks.