Can't you continue working while H-1B petition is pending? I have heard that in case of OPT to H-1B transition one can continue working while the petition is pending. But don't know exactly about CPT to H-1B. Otherwise, I think it is best to go home and come back after H-1B is approved because unauthorized stay will be detrimental to any type of your petitions to USCIS in the future. I would go home and come back to work with a visa once H-1B is approved. Most importantly you need to make sure that your employer/adviser is willing to extend your job.