Figured it out! The function I needed to hook is called “the_content”, because that’s the post content that is pulled directly from the database.
I added this code into the functions.php file for my theme.
function force_https_the_content($content) {
if ( is_ssl() )
{
$content = str_replace( 'src="http://', 'src="https://', $content );
}
return $content;
}
add_filter('the_content', 'force_https_the_content');