How can I show a parent page's field on all subpages?
For posterity, here’s the solution I came up with.

I turned my Banner Image into its own content type, used the nodeblock module so it would automatically be usable as a block, and then just scoped that block to myParentPage and myParentPage/*.

It’s not the elegant solution I wanted, I was hoping to give the user a one step process that would also keep them from creating top level pages without a banner image. But it gets the job done, so I’m happy enough.

Thank you Kevin for getting me on the right track!