I went through your requirements and looks like this requires a lot of custom code to be written to accomplish this. Currently we cannot accomplish this with the theme; will need creating custom page templates in WordPress.
Only one thing I can suggest to you is to create multiple pages, one each for each portfolio category using portfolio shortcodes as explained here –
Then you will need to create another page with handwritten HTML content that lists the links to all these category pages with a thumbnail associated with this link related to linked category page (there is no way to associate a thumbnail to a category currently in WP that I know of). When the user clicks on this link/thumbnail, that person can navigate to the respective portfolio category page which will have lightbox support for the items listed there.