As far as I know there's no way to add custom headers without reaching in to Swift Mailer.
Try something like this.
$message->getSwiftMessage()->getHeaders()->addTextHeader('X-Tags', 'tag1 tag2 tag3');
It doesn't look pretty but from looking through the source that should do the trick.
As pointed out in the comments below the getSwiftMessage
method isn't required as there is an __call
magic method on the Illuminate\Mail\Message
class that I overlooked.
$message->getHeaders()->addTextHeader('X-Tags', 'tag1 tag2 tag3');