OK, here's more info about what's wrong, and a solution.

I used additional parameter logging to determine that no matter how I adjust the parameters of the inner call to 
```
mlflow.start_run()
```

the `experiment_id` parameter of the child runs differs from that of the parent runs.  It ignores `nested=True`, it ignores passing in a value of `experiment_id`, and it sets its own child `experiment_id` to a value corresponding to a new Experiment page named the same as the name of the notebook.  Therefore, since parent and children have conflicting experiment_id values, they don't group together in the GUI.

That's pretty annoying.

However, the whole problem goes away if I set an `experiment_id` value in a global sense, back at the beginning.  Specifically, in the block that sets and uses EXPERIMENT_NAME, add one more line of code at the end:
```
mlflow.set_experiment(experiment_id=experiment_id)
```
and then everything works exactly as it should.  The child runs show up as nested under the parent run in my personal Experiment space.