I feel like such an idiot!! I was trouble-shooting this last night and I guess I removed the featured image for the news page…so, of course, the image wasn’t showing up!
I added the featured image and the following code:
<?php if(is_home()) { ?>
<?php
$page_for_posts = get_option( 'page_for_posts' );
echo get_the_post_thumbnail($page_for_posts, 'large');
?>
<?php } ?>
Now, everything works as expected (Note: cross-posted from, and issue resolved in, the wordpress.org support forums.)