First and foremost, my advice would be to call Microsoft and open a support ticket. Since this is a production user database that has been marked by SQL Server as a system database, you want to be overly cautious no matter what you try.

That being said, I've been able to re-create the problem and resolve it in a TEST environment. If you configure a SQL server for distribution (right click on the Replication folder and select Configure Distribution), you can manually enter in the name of a user database for the "distribution database name". It defaults to "distribution".

I manually entered the name of a user database and then completed the wizard. Afterwards, I confirmed that my user database was moved under the system database folder in SSMS.