Your problem is you are using the wrong tools. Thunderbird and your existing mail provider are not the right tools for the job. When you only tool you own is a hammer, everything looks like a nail.

For sending mail of the kind you are doing you need a dedicated mailing house, they make deliverability better and will not see you blacklisted as a spammer which is highly likely if you are sending unsolicited or unwelcome mail to consumers. That you have to limit your activities to less than 30 per hour says you are working very close to being outside the terms of use for your mail provider.

The Thunderbird project team used to use mailchimp for their mass mailing list needs. Even though they make a mail client, because an email client is not the right tool for mailings involving thousands of recipients.

A google search for "bulk email providers" returns about 24 obviously larger or advertising providers in a grid or you could try one of the "best" web pages for reviews of providers.

I am on a MAILMAN email server which is designed to take larger volume of emails. At 30 per hour I am well below the threshold.

I am not interested in mailchimp and other email providers. Just wanted to see if there is a solution through Thunderbird.

I will continue to do the SEND LATER manually.

I concur with Matt. MAILMAN is usually offered on self-hosted sites and does not enjoy the features of the professional sites. For example, one of the key features that I discovered with such services is awareness of who, if anyone, is reading what is being sent.

I can get that info from my cPanel under EMAIL DELIVERABILITY and that's good enough for me.