If self-hosting the app is interesting to you (it's much like running your own copy of Wordpress), consider Dada Mail - I'm the developer. It supports sending locally via sendmail, SMTP, as well as via Amazon SES.
I would suggest SES, as deliverability is great, and headaches are less. If $0.10 per 1k messages is too much to pay, sending using your local mail server is probably free, so long as you send below any hourly limitations that are set for you (Dada Mail makes that easy to do)
Dada Mail is free up to 3 lists, and 1,000 subscribers per list, after that, Go Pro. You can import an existing list, easily.
Dada Mail is a project I've been working on since I was a Freshman in College (and yeah: started it in my dorm room) 15 years ago. Still work on it, almost daily!
I've used dada mail (http://dadamailproject.com/) to help me maintain my email list, clean it up, and allows the user to unsub.
It also gives you a bunch of analytics (such as how many people opened your email, and did they click any links in the email), any how many people are subscribing your email list.
There are several open source mailing list management software programs:
I think for your use case, the best solution would be to use dadamail.net+Amazon SES, and pay a one time fee ($250) to have the developer install it for you:
http://dadamailproject.com/installation/request.html
That way, you can't be booted off, because it will be running on your own server. And no ongoing licensing fees (though you can buy a support contract).
If you have the technical chops, you can also install the software yourself for free. And there's no mailing list quotas in the open source version.