The cheapest way to do what you want is to use a custom domain name, add it to Heroku, then verify your domain with mailgun.
You can add custom domains to your Heroku app by running: heroku domains:add www.mydomain.com
Once you've done this (and updated your DNS provider to point to yourapp.herokuapp.com
, you can then modify your DNS records for Mailgun to verify your domain.
Once you have that working, you should be good!
Since you can't modify Heroku's DNS servers, you need to do it this way.