Hi Chris.
Sorry I was a little confused with your question and would like to first confirm with you:
I just subscribed to Office365, and am using my exchange account, just for receiving forwarded mail from a third party server.
Did you mean you are using Exchange Online? Do you have an Exchange On-Premises server?
I will never use my exchange account for sending mail.
So for sending mail, would it be possible to change the Exchange settings to send thru SMTP instead?
Did you mean you would like to route outbound mail from Exchange to the third party server and use the third party server to send mail?
If it is the case, you may create a send connector to route mails to the third party server.
Here are two links for your reference:
If you are using Exchange On-premises server: Create a Send connector to route outbound mail through a smart host
If you are using Exchange Online: Set up connectors to route mail between Microsoft 365 or Office 365 and your own email servers
If I misunderstood your question, please feel free to correct me.
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