Using the example that Vic posted I managed to get something working with a bit of fiddling.
This looks pretty close to what you want.
It will work with any number of slides automatically without changing the css, The only manual thing to do is to add the altlinks by hand.
The above links are only visible when js is turned off and use the fragment identifier to rotate the content.
<p id="nojs" class="altlinks"><a href="#slide1">Slide 1</a> | <a href="#slide2">Slide 2</a> | <a href="#slide3">Slide 3</a></p>
They suffer from the same problem as the existing one in that if JS is turned off and the page is resized while you have clicked one of the slides then as you open the page the scroll position is altered and a previous slide can be seen. Once you click the link again then it clicks back to normal.
I believe this would be a problem with any fragment identifier and overflow method used in a similar way and don't see a solution (unless someone else can see a different way to do this). If the slide had a fixed height then we could get around this but that would ruin the fluid nature of the slide.