As your message stated, it is the server that is stating too many recipients. That implies that the email provider has imposed that limit, not thunderbird.

Thanks for your help. I know you did. I'd like to know how to get around this limit in Thunderbird.

If the email provider has imposed a limit, Thunderbird can't bypass it. You might try the mailmerge addon and use that instead, but you then have the possibility of having email provider limit them as having sent too many emails. But that is a possibility. If you do this regularly, your best bet is to use an email mailing service, such as Mailchimp.