Just as supplementary info, here are the settings from laravel\app\config\mail.php (anonymized, of course):

'driver' => 'smtp',
'host' => 'XX.XXX.XX.XXX',
'port' => 993,
'from' => array('address' => '[email protected]', 'name' => 'EPHY System'),
'encryption' => 'ssl',
'username' => 'examplename',
'password' => 'example',
'sendmail' => '/usr/sbin/sendmail -bs',
'pretend' => false,

I just want to point out that this is a piece of built-in Laravel code that's apparently failing without generating any sort of error message. Regardless of what's actually going wrong I'd think it would be desirable to pin it down so that appropriate smoke signals can be generated when it happens in the future. I guess I'll report back if I ever figure it out.

https://github.com/laravel/framework/blob/master/src/Illuminate/Mail/Mailer.php#L109

This class is a simple wrapper for Swiftmailer, you could try making sure you have all of the Swiftmailer debugging options enabled and then try setting break points throughout that class to see where it gets stuck. To isolate if it's SMTP causing the problem you could also try switching to using the native mail function temporarily (just switch it out in the config).