Use 'Search Api Attachments' file extractor in my own custom 'Search Api' processor plugin
I was able to use the search api attachments file extractor by extending it.

The FilesExtractor class itself was a processor plugin. So I was able to access all the functionality by using 

class BodyFieldAttachments extends 
\Drupal\search_api_attachments\Plugin\search_api\processor\FilesExtractor


instead of

class BodyFieldAttachments extends ProcessorPluginBase


Then I could just override the specific functions that need to be overwritten while having access to all the functionality the search api attachment plugin had.