Hello Sir,
I'll WP & MailerLite expert here, I can do everything you want to switch over to MailerLite including: email sending/creation, subscription management, switching referral program to sparkloop, email verification feature with MailerCheck and more, I have extensive experience building custom features using APIs. I can assure there would be no downtime to live site as we can setup staging site and work on that and make unlimited tests.
Please let me know the current site url so I can check and give you ultimate cost to complete everything after a clear discussion.
I've worked for you in past and will love to have a chance again,
Thank you,
Sumon