Quick hack to get the job done, in case anyone else needs to do this:
add_action('add_meta_boxes', function() {
add_action('admin_head', function() {
echo <<<EOS
<style type="text/css">
#visibility {
display: none;
}
</style>
EOS;
});
});
add_action('restrict_manage_posts', function() {
echo <<<EOS
<script type="text/javascript">
jQuery(document).ready(function($) {
$("input[name="keep_private"]").parents("div.inline-edit-group:first").hide();
});
</script>
EOS;
});
(Still curious to know if there’s a better way.)