While it is possible to use MX records with a different provider (And it has been done), I personally have never done it. Others may be able to help you if you want to keep it this way.
If you want, you can switch to a method (also free) that I know works. And that is Cloudflare. You can set it up using the guide below. Once you finish that, their is an email tab in the sidebar, and just follow the prompts to set it up.
Feel free to let me know if you have any questions!