your H1 will be effective only from October. technically you dont have a H1 so far. If you enroll somewhere to get a I20, it will not affect your H1 at all. I did the same thing some time back (after my OPT expired). before you enroll in any schools/institutions, I would suggest you to check with USCIS regarding the status of your OPT (you can also talk to your INTL student advisor and see what he/she says). It seems that you still have about a month. So take your time, find out more about the status of your OPT and then if that doesnt seem to work enroll somewhere. But dont wait too long. You will need time to talk to schools. they will ask for soem time to process ur applciations, transfer your sevis etc,....good luck.