Okay, I found my problem. I initially started out using a custom ResourceConfig, because I was using grizzly. For some reason, I was under the impression that in a servlet environment it would simply be detected. So, I didn't put 2 and 2 together regarding web.xml configuration vs ResourceConfig configuration. Since I had some of the features configured in web.xml, and they were working, but I also had them in ResourceConfig, I was under the impression my ResourceConfig was working.
I'm guessing that the docs can be updated to be more clear on ResourceConfig loading, but I'm not sure how yet. I'll think about it, and see if I can change the docbook stuff to save someone else the grief. Overall, the documentation is quite good, it's just a bit glitchy for a newb. :D
Anyhow, I've now removed all my configs from web.xml, and replaced them with...
<init-param>
<param-name>javax.ws.rs.Application</param-name>
<param-value>com.example.MyResourceConfig</param-value>
</init-param>
And all my problems vanished.
I'm on research and study leave one week out of every 3, so I'll probably work on updating those docs in a couple of weeks.