Originally Posted by
msett
... Could we pick up our JR Pass Saturday at Narita and tell them we want to start using it on Sunday? ...
This is exactly what you should do. Take care of Pass activation and shinkansen seat reservations to Kyoto all at the NRT train station or service center. They will take the exchange order you already have, change it for the actual Rail Pass and set the Rail Pass to be effective for whatever dates you tell them.