I am not sure, if you are still awaiting response from USCIS. You will need to check with your DSO, just call them, if you do not have response or visit them and get it sorted out. As you said, one option is that you can go to India and get the F1 stamped. While, what you said is logically correct, I am not sure, how it pans out. Usually, COS is abandoned, if you leave the country... You can always schedule an appointment with USCIS local office and seek their advice with an in-person appointment.