Enabling Journaling in Exchange Online

Solution 1:

This is correct. You can't journal to an Exchange Online mailbox. You'll need to use an external mailbox or journaling service/appliance.

https://docs.microsoft.com/en-us/exchange/security-and-compliance/journaling/configure-journaling

If this is a business/company requirement then don't try to "trick out" Exchange Online with BCC'ing or any other method. Use an appropriate journaling service. You don't want to be in a position of having to explain to the customer why you can't retrieve an email for them if they have a need (legal) for the email in question. Explain to them that if this is a business/company requirement that there will be additional costs involved.