Echo an array / date time object in timestamp format

You're looking for:

echo $date['start']->format('Y-m-d H:i:s');

I believe... Check all possible formats here, on the manual page
Don't let the dump fool you, the DateTime object hasn't got a public date property, as you can see here. It does, however, have a getTimestamp method, which returns an int, just like time() does, cf the manual.
You can use any of the predefined constants (all strings, representing standard formats), for example:

echo $data['end']->format(DateTime::W3C);//echoes Y-m-dTH:i:s+01:00)
//or, a cookie-formatted time:
echo $data['end']->format(DateTime::COOKIE);//Wednesday, 02-Oct-13 12:42:01 GMT

note: I based the +01:00 and GMT on your dump, showing London as your timezone...

So:

$now = new DateTime;
$timestamp = time();
echo $now->getTimetamp(), ' ~= ', $now;//give or take, it might be 1 second less
echo $now->format('c'), ' or ', $now->format('Y-m-d H:i:s');

Read the manual, play around with it for a while, and you'll soon find the DateTime class, and all of it's related classes (like DateInterval, DateTimeImmutable and such (full list here)) are very handy things indeed...

I've put together a little codepad as an example, here's the code:

$date = new DateTime('now', new DateTimeZone('Europe/London'));
$now = time();
if (!method_exists($date, 'getTimestamp'))
{//codepad runs <PHP5.3, so getTimestamp method isn't implemented
    class MyDate extends DateTime
    {//bad practice, extending core objects, but just as an example:
        const MY_DATE_FORMAT = 'Y-m-d H:i:s';
        const MY_DATE_TIMESTAMP = 'U';
        public function __construct(DateTime $date)
        {
            parent::__construct($date->format(self::MY_DATE_FORMAT), $date->getTimezone());
        }
        /**
         * Add getTimestamp method, for >5.3
         * @return int
         **/
        public function getTimestamp()
        {//immediatly go to parent, don't use child format method (faster)
            return (int) parent::format(self::MY_DATE_TIMESTAMP);
        }
        /**
         * override format method, sets default value for format
         * @return string
         **/
        public function format($format = self::MY_FORMAT)
        {//just as an example, have a default format
            return parent::format($format);
        }
    }
    $date = new MyDate($date);
}
echo $date->format(DateTime::W3C), PHP_EOL
     ,$date->format(DateTime::COOKIE), PHP_EOL
     ,$date->getTimestamp(), ' ~= ', $now;