I went with a mix of geneven's and kamiwey's approaches : a "home screen" that has links to the other three, and the other three have a single link to home. Always two clicks max to destination.

The button images are thumbnails of the desktops themselves. I have made them specialized and different enough to be easily recognizable.

I love the new system, I was bored with swiping this way and that to find my stuff :-)

Once again thanks to Nicolai for this very neat widget !