I work on the Mandrill team and saw your question and thought I could help. I don't have access to the MailChimp support queue, but I thought I'd add some detail on using Mandrill since Mandrill is probably a good fit for the type of emails you're sending.
With MailChimp, because it's designed for bulk email, you absolutely have to allow recipients to unsubscribe. There's not a way to remove the unsubscribe link and MailChimp's system is designed to detect when an unsubscribe link isn't present and stop the emails from being sent. Adding back people who have previously unsubscribed is problematic, and the MailChimp list management functions are designed to prevent adding people back who have unsubscribed in the past.
Mandrill, however, doesn't strictly require an unsubscribe link because it typically doesn't make sense for people to unsubscribe from transactional and one-time emails or notifications. You can send any legal, non-spam messages through Mandrill (including bulk email). If you're sending bulk, you would just need to be aware of and abide by the laws and regulations that govern your emails (such as requirements for unsubscribe links).
You can send to more than one person at a time with Mandrill, as described here: https://mandrill.zendesk.com/hc/en-us/articles/205582557-Can-I-send-to-more-than-one-recipient-at-a-time-
If you're using the SMTP integration, you can specify up to 1000 recipients for your To: field. If you're using the API, you can specify as many recipients as needed in the 'to' array: https://mandrillapp.com/api/docs/messages.html#method=send
Feel free to email Mandrill support by clicking on the 'Submit a Request' link at help.mandrill.com if you need more info on using Mandrill.