Mail for a domain with the ability to send newsletters?

Question

Email Marketing

It is necessary to park under the domain on a third-party service in order to carry out mailing through it. The site will completely collect and send the newsletter.
At the moment, the domain itself is parked on Yandex, and we use it (there are a lot of boxes), in connection with this, it is not possible to transfer the domain to another service, we decided to do this with a subdomain.
Problem. From the site, the mailing goes through SMTP, but Yandex, as it saw 300 mailboxes to which you need to send letters, at the same moment blocks the mailbox for a day.
The mailing takes place once a week or two (not often), the recipients are about 300 mailboxes, and applications from the site (call back, etc. - also not often).
Advise the service, maybe paid (with reasonable prices)?
ps I googled on my own, but there is sadness, trouble, without outside help to figure it out.

Answer 1

Try Mailgun

Answer 2

Or sendgrid

Answer 3

Amazon ses