Just a small boo-boo, really. Here’s the code, and I’m attaching a screenshot.

piklist('field', array(
    'type' => 'file',
	'field' => 'home_feature_image',
	'label' => 'Feature Image for the home page',
	'description' => 'An image will be chosen randomly each time the page loads',
	'options' => array(
		'modal_title' => 'Add File(s)',
		'button' => 'Add',
	),
));

Ironically, I’m rewriting this field and it will no longer be an issue. 😉