Well, it seems options are a bit thin on the ground for using multiple covers per book
so unless you would like to write your own plugin to handle it, you might just be out of luck.
That being the case, the best suggestion I can offer is to use the FFDL integration.
Perhaps after downloading the book with a custom cover, you can manually do a bulk download of covers (although I don't see FanFiction on the list of metadata sources, Google Images *might* provide something) and set the cover image in calibre. It will not be updated in the MOBI, because MOBI doesn't support cover metadata properly.