Your school is really stupid. But I still think you will be OK. Because USCIS has approved your F-1 instatement, they of course knew the duration you were out of F-1 status (from 12/99-04/02). After they approved your F-1 instatement, you should have no status problem. So,just send the reinstatement I-20, and all other I-20 Forms, OPT/EAD to USCIS for the RFE.
But if you still feel unsafe and if your current status is H-1 or other non-immigration status (Not AOS), you may go to Mexico or Canada to get an H-1 visa (or other visa) to come back as soon as possible. Once you do that, all the unlawful presence will be cancelled.