Within the group (column), the next and previous slides can be found from the current one using jQuery's aptly named .next() and .prev(). So to go to the next slide (i.e. down"down" on your site), you could do something like:
Anyway, these are just some ideas based on your chat with Tomalak and the site's HTML. There are obviously things that can be optimized (e.g. caching slide/group indices using .data()). Just consider it food for thought.
Here's a simple jsfiddle just to demonstrate the DOM traversal stuff