With those volumes, there is no way you are going to be able to get by without using an SMS shortcode. Even if you could technically get it to work with a regular number, I suspect you would be shutdown as a spammer pumping out so many messages on a regular phone number.
A short code will let you send at at least 30 messages per second (1800/minute), and supposedly they can up that for you if you have a justified need.
https://www.twilio.com/sms/shortcodes
and this: https://www.twilio.com/help/faq/sms/can-my-twilio-sms-messages-be-blacklisted-as-spam
Can my Twilio SMS messages be blacklisted as spam?
Recipient carriers always reserve the right to filter out messages from certain numbers, and routinely do so to protect their users from spam.
If you’ll be sending SMS messages as part of a bulk campaign (with 30 or more identical or similar messages going out within a few minutes), we discourage you from using regular 10-digit numbers. Instead, we highly recommend using an SMS short code.