Hi,@Rider, Justin
Thanks for posting your question in the Microsoft Q&A forum.
According to your description, here are my suggestions:
In Exchange Online, follow the documentation to set up a connector, but when configuring the connector, you need to use the private IP address or internal DNS name of your internal relay server instead of the public address.
Regarding Azure question, it is separate from Exchange Online. In order to better solve your problem, I will add Azure tag to your problem.
Best