BoundRequestContext should work - I used it once in a small open source lib to integrate Quartz scheduler  with no problems. Could you describe your "remaining problems" more thoroughly? Anyway you could also try DeltaSpike's ContextControl feature . I don't know of any trick that could help here.
The only problem was that we were trying to use a sessionscoped object inside the job and jetty was throwing NPE about its SessionManager. In my opinion, maybe, weld could provide a way to full eager initialization object... The Lazy initialization is a problem for cases like that...