Never mind, I realized that using conditional logic to hide the field unless the options that make it required are chosen works how I want it to.
For future reference, given my example above:
Making the 'Character' field required and setting the conditional logic to display the 'Character' field only when 'Actor' or 'Actress' is chosen in the select field makes the 'Character' field required only when 'Actor' or 'Actress' is chosen.
This allows the post to be successfully saved when 'Director' or 'Writer' is chosen, but no 'Character' has been set (because even though the field is set to required the field is hidden and, therefore, not required in this instance).
If 'Actor' or 'Actress' is chosen, then the 'Character' field is displayed and requires a value for the post to be successfully saved.
Hope this helps anyone searching for this functionality in the future.