Your application will be processed by AMCAS much faster if your school sends the transcript request form with it. I'm sure your school's registrar has a fax number, this is the quickest way to get the forms in. Fax both the school's transcript request form and the AMCAS transcript request form. If the school asks for a deadline, pick July 1st. That gives the school enough time to process your request and send out the transcript, but is soon enough that they (hopefully) won't delay processing.