I just tried to remove the scope-related hacks in -jsr352-jberet, and it turns out they are not necessary. It makes sense, since the default scope in CDI is "dependent" (i.e. one instance per request).
I probably got confused when trying to make things work even though there was an @Singleton annotation on every batch artifact.
Anyway, this means that the only thing the -jsr-jberet artifact actually provides is the CDI integration. So it could work with other JEE application servers after all, and if so we should consider providing a -jsr352-cdi artifact that could be used with any JEE application server.