Visa Issues (Germany)

Our school recently told us that they have received word that our visas are completed and paid for, but my family needs to travel to the German Consulate in Chicago (6 hours away) to complete the procedure. When we attempt to set a schedule with the consulate, they tell us that we need to start the application online. They don't seem to care when we tell them everything has already been completed.

Why this matters: school starts September 1st. The consulate is booked solid for 6 weeks. The visa states it needs to be finalized in the next 3 weeks.

What the heck am I supposed to do?