You do realise that in order to send 600,000 emails in 3 hours you require a system that can send 146,000,000 emails a month, irrespective that you only want to send that number per day over 3 hours.
Taking your figures you need a system capable of sending 200,000 per hour x 730 hours in a month = 146,000,000
There's a reason why the likes of Mailchimp charge what they do.
If you have the ability to spin up multiple servers to send what you need then MW can cope with it.
Your limiting factor is PHP, however you can greatly improve its performance using php-fpm.
Remote connections will always be the key factor if that is how you send emails. You either need to send via an API or through your own MTA which will require a lot of work regarding IP address reputation.