You will get some trouble if you apply for the green card or exchange your status.USCIS should check your payroll without cap date when you are approved H-1B.You must talk with the attoney who applied for your H-1B and your employer.I met some cases which were paid earlier than the date H-1b approved.But never head the case like you.You should understand the USCIS has no way to explain your case.Good luck!!