Turn to a hosting company that doesn't have limitations regarding sent mail number.

I believe if you are going to sell out more then 1000 emails per hour on shared wweb hosting account your web host will never allow you to do so.

I was researching newsletter email hosting hosting providers, and would be the list (certainly incomplete) that I got: Aweber, GetResponse, phplist, MailChimp, iContact, imnicamail, constantcontact, madmimi.

So much is not allowed by any company.

If you do so then it would be spam as well.