What would you use here for your agitation? A brush or sponge would be too agressive. I would use a white pad for a buffer. You know the way the centre part pops out. Use this little circular piece with some Cif. Wet your pad, apply the Cif and go at it in a circular motion. Then with a micro fibre cloth wrung out in hot water, get your leading edge going in figure 8 rotation to get the cif out. Failing this, maybe do a leather cleaning course and get a spotter kit for that if there is one.