JBoss throws the following exception when resources.war (produced by dna-web-jcr-rest-war) is deployed:

14:01:48,969 ERROR [[Resteasy]] Servlet.service() for servlet Resteasy threw exception
javax.servlet.ServletException: non-HTTP request or response
at javax.servlet.http.HttpServlet.service(HttpServlet.java:818)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:290)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:206)
at org.jboss.web.tomcat.filters.ReplyHeaderFilter.doFilter(ReplyHeaderFilter.java:96)
etc...

The error message is fairly cryptic, but the problem seems to be that the war file and JBoss itself provides different versions of servlet-api.jar. Using the provided scope for dna-web-jcr-rest's dependency on servlet-api fixes the problem by removing servlet-api.jar from the war file.