Hi Brittany -
If I am understanding correctly, you want to update what is visible in the Overview section of a template when the project is opened using it?
You can update/add to the fields in the Overview section and they will then display when you open a project from that Template. Unfortunately, you can not remove any areas/sections of the Overview section at the Project Template level for them to be the same when a project is opened - what is visible in the Overview area of any object can only be done through Layout Templates.