I've resolved this issue. In fact their was no actual issue. I just hadn't configed the card correctly.

My test embed cards do not swap data source. The drill path limit of 3 even occurs even if the 4th drill down is the view of the data. From your comment I will build a very basic drill down card with a single source and if I still get the issue will post the URL to it here.

I logged a support case with Domo support and a hotfix was applied a week later which resolved these issues.