If you set the input phase to "hue" and the modify to "hue" as well, your original image should appear unchanged. Then you can animate the phase rotation and see if that gets you what you want.
What's the best method of cycling through a gradient? I'm using hue and saturation and cycling the master hue but some of the interpolated colours are pretty ugly. Is there a way to control those mid cycle colours? I need to animate the hue forwards only as I need to suggest that the colours are moving forwards.