Here's no sense in creating standalone site with stories. Do you really want to answer abuses and involve lawyers? KA contains any stories. With minors. With zoo. With rape, snuff and other themes. ASSTR team already have experience to deal with possible complains.
Just create new collection, like KA. Donate to ASSTR, if it necessary. For accepting new stories, search engine, tag engine you can create external site, that will not contain any dangerous content, only code, forms for authors, tag and search index and links to stories in new collection on ASSTR.
Joomla, Wordpress and other CMS is not needed for ASSTR and other story sites. Their content is mostly static. To deliver such content to your browser, webserver just read plain text file, write it to socket and - you got it, you can read it. Static site is optimal for reduce costs. It's very hard to hack such site. It just works.