My spouse who is on L1 Visa has to return to his parent company and its payroll in between projects. Is it possible for me to continue to stay and work in the USA for the period that he is away (6 months)?
If the L1 is gone for a considerable period - 6 months - he is not in valid L status even if his visa is still valid. As a derivative your status is attached to his.
Since your main beneficiary is leaving you will not be able to be in legal status as your status is attached to his.
He must be in valid legal status to confer the same valid legal status on your, you are the derivative beneficiary of his petition.