(I found all this out because I called the authorization department back a second time when they didn't call me back after my first call as I was told they would.)
At this point apparently it's "in medical review" at the insurance company and there's nothing that can be done to speed that up.
Now apparently we're going to wait another couple hours to see what happens, and if still hasn't been approved I'm going to have to cancel and reschedule the procedure.