[EDIT: I have updated the app since this post was written, and it is now over here: Basic Test Management app and sharing seems to work now]
So I managed to make something useful using the automatic relations feature: a rudimentary test management app.
The idea is that a Test Case has several ordered Steps (with Action and Expected Result fields), and is linked to one or more Test Executions.
The Test Execution also links to a set of (ordered) Step Results (which have an Actual Result field, to be filled in by the tester when the test is run).
Then by auto-linking the Step Results to the Steps (based on the test case and order number) it’s easy to have a table view for each execution showing action/expected result/actual result for each step.
I also added a bit of logic so that it’s possible to see which execution is the latest for each test case, plus a summary report of all testing.
I hope people will have a play with it and give feedback.
[edit: I have tried to import the app into another instance of fibery and I get an error message:
so hopefully @mdubakov or the team can figure out what’s going on. I think it may be a bug in sharing apps that contain automatic relations]
For the next iteration, I was thinking of adding an action button for the Test Case (‘Execute Test’) which would automatically create a Test Execution and all the necessary Step Result entities, so that a tester only needs to enter the Actual Result data 
There are still some practical issues to be considered/fixed, such as how to handle changes to the test case after it has been executed, but it seems that versioning might be coming from the fibery team at some point, so I won’t try and tackle it just yet