Where is it you’re stumbling?
Are you trying to set up the same domain [doubtion.com] at both google apps and one of the recommended third parties?
You need to use a subdomain for email coming from Discourse, it doesn’t matter what, it just needs to be different. Common suggestions:
board.doubtion.com
forum.doubtion.com
discourse.doubtion.com
community.doubtion.com
And configure the MX records for the mail service routing from your board under that subdomain.
If two separate services are both set up with the same mail domain, they won’t know the other exists to route email there. So, if you had tried to use mailgun at doubtion.com it wouldn’t be able to send email to your google apps mailbox. It would have thought it was doubtion.com.