Can J1 Visa be used for short-term work purpose

I am Indian, and I moved to US from another country on a student exchange programme. I have a F1 Visa which is valid for 5 years but I only have another 2 months to graduate and after which I will have to leave the country. I want to stay here and work but since I have been here for only 4 months now, so I am not entitled for an OPT. Nither I can apply for jobs as even the H-1B cap seems to be over so no employer can sponsor me. What I have found so far is that I can enroll into some other study program (may be another Masters) and try to work alongside, but is that my only option? Could I use a J1 Visa for some short time work until H1-B opens up again? Does someone here happens to know of other good ways to extend stay and be able to work, legally though.