Has anyone replaced a listserv with a WP or other solution?

I have a client who's been on traditional listserv for over 10 years. Actually they have 3 lists and the big list has 800 members.

Members submit by email and a moderator approves messages which in turn go out to all 800 members.

The service is being discontinued and they wondered if there was a plugin for WordPress... and the answer is no.

They aren't opposed to the idea of using a web based form to submit content and then photos could be added. But we also have to think about 1500 emails per day.
Also this information is private so a WP site would need to become a membership site and now we are managing members

Maybe a web form to MailChimp and using segments we could combine 3 lists into one?

Sorry for rambling but I wanted to post my thoughts and see if anyone else has had experience with a complete solution to replace a listserv?

Thanks in advance for any input.