How can I reduce the length of the featured content excerpt that is contained within the slider?
Featured slider supports WordPress Excerpts function which means that you can set it manually as well. If you want to make it shorter just add necessary content to the Excerpt box right below Post Edit screen.
If you can’t see Excerpt function underneath the post you can enable it via Screen Options located in upper right corner in Post Edit screen.
Additionally you can set excerpt filter to trim them automatically. Additional information about it you can read here: http://codex.wordpress.org/Function_Reference/the_excerpt
Featured slider Excerpt function is located in header-extensions.php located in theme folder → library → structure.