Optimize daily newsletter sending for 1,000 recipients

We have a wordpress website hosted on a shared server, with inimum capabilities to send daily and weekly emails to subbscribers (around 1,000). The server does not allow to send more than 30 mails per minute. There are also sometimes special emails sent to the whole database, so there should be the possibility to manage in one single day: - 1 daily email sent to users - 1 weekly email sent to some users (they can select if they want to receive daily or weekly digest) - to mitigate the risk we can choose to send the weekly digest on sunday and not send the daily email on Sunday - 1 email for an invitation to all, sent 5 / 10 times per year We are struggling to send all these emails with this limitation. We are looking for somebody experimented in this field, to set up a long-term fix.