How do I reference the front page’s parent Page object?

You can get the ID of the front page via get_option( 'page_on_front' ). (See also: WordPress option reference.)

From there, you can query the page object via get_post():

$frontpage = get_post( get_option( 'page_on_front' ) );

Then the content is in the $frontpage object:

$content = $frontpage->post_content;