I am the Co-founder of Grizly.com. We are beginning to scale up our email marketing strategy and are getting ~1,000 emails/day. I think it will be closer to 10K leads/day at scale. We send each lead an autoresponder of ~20 emails/month. So we'll likely be sending millions of emails a month by Q2. What is the best and safest software to manage our email campaigns? Mailchimp and SendGrid both seem too expensive.
I will recommend you to use EasySendy, Vero or AutoPilot. You should know anyway than sending emails is expensive and that should be considerate in your costs.
did you try your hands on mailget, aweber, moosend, campaign monitor. I think sharpspring mail+ or mailerlite would help you since you want to send such a large bulk of emails.
Make sure your spf and dkim is setup - in short sender policy framework which is being managed by sender score an IP reputation tool - would help to avoid getting your emails in spam