Looks like I'm a little late to this thread. IDK why email isn't a public forum and is hidden in the JV section but w/e.
To send 400K in a reasonable amount of time you'll need to work with either your own setup or someone who has the tools to streamline the process for you. Mailing is still by far the best way to promote anything but there are challenges involved, such as building up rep and maintaining delivery performance. I'll drop a freebie for you:
If your list is mostly one or two domains, you will not be able to send at a high rate. In the past you could increase speed by stacking IP addresses, but if you do this today, it will cause the IP block (the entire /24) to get banned...so you are limited to 2-4 IPs per domain for sending NON-TRANSACTIONAL email.
The guy here who posted the mailer king sending 3,700 per minute was not sending at that volume to hotmail or gmail only. The list has to have a good diversity of domains, called GI (General Internet). You can blast out a lot of mail to a GI list but at the same time it has a high chance of getting your IPs on spamhaus because it will almost certainly be full of traps. So unless you are using a mailing system like DGMS, which profiles each domain and does deep DNS queries to identify the true owners of particular domains in real time, you aren't going to be sending much of anything.
The other thing that you need to understand when mailing is that you will need AT LEAST two weeks from the day you start mailing to warm your IPs and domains. While you are doing this, you can't be sending promo emails. You have to send something mail without links or anything. A good choose would be a "welcome" email, like "thank you for registering with us". Or 'email verification'.
Once you start mailing, you shouldn't stop. You should mail CONSISTENTLY each day. You can't start and stop or you will overall hurt your rep. That means your daily target volume should be LIST SIZE divided by 5. If your list is 400K, then the max you should send is 80K per day (if your goal is to maintain rep). If you have a small list and resend to the same recipients each day, it will ultimately cause your rep to drop.
I've been doing this for over 10 years and while most of my colleagues have disappeared, I'm still around.

That is a testament to the fact that my ways of mailing are effective. BHW has decent people on there but for every one honest person there's 20 scammers/bullshitters who promise a lot and either don't deliver or just rip you off. It is wise to make a contact list of honorable people that you meet, either on BHW or anywhere else.