I don't think this will work, based on a quick glance at the tapestry-resteasy code.
The @Inject annotation is part of tapestry-ioc; if a class is not instantiated by Tapestry, the @Inject annotation is not honored.
Filters defined in web.xml
are instantiated by the servlet container (Jetty, Tomcat, etc.) which do not have any special knowledge of Tapestry and Tapestry annotations.
I think you will be better off contributing a filter into Tapestry's HttpServletRequestHandler or RequestHandler pipelines (see their JavaDoc). I'm not sure how you can gain access to the ContainerRequestContext, however.