Pre-populate default values into a form to edit a new entity
I think I found what the problem was. From the documentation and Drupal code it became clear that what I did in the form ought to be correct: field_attach_form should properly load all fields.

Which led to the fact that it must be the creation of the entity that is incorrect and not the actual form loading of the entity fields.

While examining the entity class I use, I came to the conclusion that the example code I used to build this entity wasn't complete. Upon first creating an instance of the entity, the code should not only save the entity data itself, but it should also call field_attach_insert. Just as it should call field_attach_update whenever the metadata entity exists already but is saved again (updated).

Upon adding this, the field_attach_form call now "magically" loaded the proper default values into the form.

Eureka.