PHPMailer with domain-based Gmail account - php

Question

I've been using PHPMailer for years and have been pretty happy with it, but now I'm trying to get a contact form working with an email address that is domain based but tied to Gmail via Google Apps. I.e. the MX record points to Google. I've added PHPMailer's Gmail example trying to get the setup to work, but at this point, I'm not connecting; I get this message:
SMTP ERROR: Failed to connect to server: Connection timed out (110)
SMTP connect() failed.
Mailer Error: SMTP connect() failed.
Here's my form processor code:
<?php
/**
* This example shows settings to use when sending via Google's Gmail servers.
*/
// CUSTOM: collect data from our web form
$name = $_REQUEST['name'];
$email = $_REQUEST['email'];
$tel = $_REQUEST['tel'];
$subject = $_REQUEST['subject'];
$message = $_REQUEST['message'];
//SMTP needs accurate times, and the PHP time zone MUST be set
//This should be done in your php.ini, but this is how to do it if you don't have access to that
//date_default_timezone_set('Etc/UTC');
require 'mailer/PHPMailerAutoload.php';
//Create a new PHPMailer instance
$mail = new PHPMailer;
//Tell PHPMailer to use SMTP
$mail->isSMTP();
//Enable SMTP debugging
// 0 = off (for production use)
// 1 = client messages
// 2 = client and server messages
$mail->SMTPDebug = 2;
//Ask for HTML-friendly debug output
$mail->Debugoutput = 'html';
//Set the hostname of the mail server
$mail->Host = 'smtp.gmail.com';
//Set the SMTP port number - 587 for authenticated TLS, a.k.a. RFC4409 SMTP submission
$mail->Port = 465;
//Set the encryption system to use - ssl (deprecated) or tls
$mail->SMTPSecure = 'ssl';
//Whether to use SMTP authentication
$mail->SMTPAuth = true;
//Username to use for SMTP authentication - use full email address for gmail
$mail->Username = "myemailaddress.com";
//Password to use for SMTP authentication
$mail->Password = "mypassword";
//Set who the message is to be sent from
//$mail->setFrom('from#example.com', 'First Last');
//Set an alternative reply-to address
//$mail->addReplyTo('replyto#example.com', 'First Last');
//Set who the message is to be sent to
$mail->addAddress('myemailaddress', 'my name');
//Set the subject line
$mail->subject = $subject;
$mail->Body = "Name : $name\n\n"
. "Email : $email\n"
. "Telephone : $tel\n"
. "Message :\n\n $message\n"
. "";
//Read an HTML message body from an external file, convert referenced images to embedded,
//convert HTML into a basic plain-text alternative body
//$mail->msgHTML(file_get_contents('contents.html'), dirname(__FILE__));
//Replace the plain text body with one created manually
//$mail->AltBody = 'This is a plain-text message body';
//Attach an image file
//$mail->addAttachment('images/phpmailer_mini.png');
//send the message, check for errors
if (!$mail->send()) {
echo "Mailer Error: " . $mail->ErrorInfo;
} else {
echo "Message sent!";
}
To answer some questions in advance: yes, SSL rather than TLS is enabled in Gmail, and the MX record is changed at the host. I also did comment out some stuff, but as far as I can tell nothing that I need to get the form to actually send.
Beyond that, I don't even qualify as a hack with PHP; my primary skills are design, HTML and CSS, so I'm probably missing something obvious....
Thanks in advance.