Thanks!
For anyone else following this, I couldn’t just add that CSS to a style sheet. I needed to create a snippet like this:
function my_acf_admin_head() {
?>
<style type="text/css">
.acf-relationship .list {height: 340px;}
</style>
<?php
}
add_action('acf/input/admin_head', 'my_acf_admin_head');