Paying for Mailchimp a small fortune is like paying for bottled water where all you need is $15/year Brita filter and just drink tap water.
Nowadays all major email providers are really good at catching spam. If you are NOT spamming then you are good to go; the key is to start small and grow from there. Do not switch overnight and send 10,000 genuine emails letting your audience know your terms of service have changed; since they don't know your IP, they will consider spam. But if you are getting your newly subscribed audience into getting emails (confirm double opt-in) from your new IP, it will take you 2 months and approx +10% daily raise in sendout to get to $1MM emails per week from your OWN IP at $5/month rate and delivery rate will be similar to those big guys that claim they have the best delivery rate (noone can guarantee you that)! Tested and confirmed!