and keeps getting pulled as the default

have you considered replacing it in the main theme directory using FTP?

No need to reply if you have.

My goal is to never touch a theme that I don’t control and I definitely do not control Twenty Seventeen! Child themes are much safer way to make your own customizations.

I found the answer in an article at Kinsta.com:

https://kinsta.com/blog/twenty-seventeen-theme/

function my_custom_header_args( $args ) {
  $args['default-image'] = get_theme_file_uri( '/assets/images/header.jpg' );
  return $args;
}
add_filter( 'twentyseventeen_custom_header_args', 'my_custom_header_args' );

And placed the corresponding image in the child theme /assests/images folder.

Hopefully, that will save anyone else some time if they want to build a child theme on Twenty Seventeen and have their own default image in the child theme!

~Bonnie