PowerBI Embedded with multiple enviroments

We are working on a feature to embed a Power BI report within our proprietary application ("App-owns-data.")  We already have it working in that we can publish the report to the Power BI service wiht our Premium License and our application can fetch an embed token that allows it to display the report to our users with row-level security applied.  We are using the DirectQuery mode so that users can make changes in the app (ie purchase things) and see the report update in real time.

The problem is that like most development shops we have many environments.  In addition to our dev environments, there are 8 QA environments, UAT environments, Staging, Demo, Sandbox, etc. etc.  And we are planning to add more and more environments as we go.  Each environment of course has its own database and copy of the application.

My question is how are we supposed to manage our PBI report such that each environment is displaying the data from its database?  From what I can see, we essentially need to create a new workspace for each environment, and then we need to publish the report from PBI desktop to each one, changing the connection string each time.

This strikes me as absurd.  It means if I make a change to the report, I need to first publish it to the dev workspace, then I need to change the data source and publish it again to the QA1 workspace, change the data source, publish to the QA2 workspace, etc. etc. 30 times over! 

Surely there is a better, more automated approach for doing this, but I cannot find any reasonable suggestions online.  How do other dev shops manage this?