Filtering part of a multi-value field in a specific view
In order to have full power over the filtering and sort order of the field inside each item, the best solution appears to be a sub-view using the views_field_view module.

https://drupal.org/project/views_field_view


Create a view that only shows the desired field (without a page display)
Add a contextual filter for the entity ID to be displayed
Add this to the parent view, setting the contextual filter to the entity ID of the current item.