Multi vs Cycle

Remember your digital Casio watch from high school? Where you had to cycle trough the different modes by pressing just a single button?

You rarely find them in UI design on the web.. heck.. I don't even know how they are called. "Cycle Buttons"? They feel cumbersome, not being able to select an option directly. So should we forget about them completely? Wait, maybe there are some rare occasions where they could come in handy. For an upcoming project, I'm in the following situation:

So I ended up using 3 of those "cycle buttons". Once you start clicking on a group, your mouse/eye don't have to move anymore. Ahh.. relaxing! And to make sure the user doesn't get lost in the cycle, there is still an indicator.