[Ted S]

You could modify every single script that sends emails to check against a volume database but not only is that a ton of work, it's also not a solution as you could potentially have emails queued up forever.

A much better solution is to move to a host that understands you offer a legitimate, mid-sized service that will send out emails to optin users. That your current host can't do this is a sign of an issue with their resources and not your site.