How do I use the RabbitMQ delayed message queue from PHP?

I'm trying to use the Delayed Message Queue for RabbitMQ from PHP, but my messages are simply disappearing.

I'm declaring the exchange with the following code:

$this->channel->exchange_declare(
    'delay',
    'x-delayed-message',
    false,  /* passive, create if exchange doesn't exist */
    true,   /* durable, persist through server reboots */
    false,  /* autodelete */
    false,  /* internal */
    false,  /* nowait */
    ['x-delayed-type' => ['S', 'direct']]);

I'm binding the queue with this code:

$this->channel->queue_declare(
    $queueName,
    false,  /* Passive */
    true,   /* Durable */
    false,  /* Exclusive */
    false   /* Auto Delete */
);
$this->channel->queue_bind($queueName, "delay", $queueName);

And I'm publishing a message with this code:

$msg = new AMQPMessage(json_encode($msgData), [
    'delivery_mode' => 2,
    'x-delay' => 5000]);
$this->channel->basic_publish($msg, 'delay', $queueName);

But the message doesn't get delayed; it's still immediately delivered. What am I missing?

From here,

The message creation should be

require_once __DIR__ . '/vendor/autoload.php';
use PhpAmqpLib\Message\AMQPMessage;
use PhpAmqpLib\Wire\AMQPTable;

$msg = new AMQPMessage($data,
            array(
                'delivery_mode' => 2, # make message persistent
                'application_headers' => new AMQPTable([
                    'x-delay' => 5000
                ])
            )
        );