I ended up just writing a function inside of my template’s index.php like this.
function fancySearchAndReplace() {
$regex = '/myregex/';
$my_posts = get_posts(array('post_type' => 'post', 'numberposts' => -1));
foreach ($my_posts as $post) {
$content = $post->post_content;
$theID = $post->ID;
$thing = get_field('thing', $theID);
$updatedContent = preg_replace($regex, $thing, $content);
wp_update_post(array(
'ID' => $theID,
'post_content' => $updatedContent,
));
}
}