Thanks for the reply! I tried that solution but it ended up changing my h1 title as well.
In case anyone was wondering, I got this working by adding the following code to my functions.php
add_filter('document_title_parts', 'replace_page_title', 10);
function replace_page_title($title) {
if( get_field('meta_title')) {
$title['title'] = get_field('meta_title');
}
return $title;
}