In order to accept your explanation I would have to assume that the bow/leading edge pressure wave is significantly different in pressure (not just size) between thick and thin leading surfaces.
I don't think so. Imagine two airstreams, one with a large entrained water droplet size, the other with a small water droplet size, flowing towards the same aerofoil. Some of the water droplets entrained in the airflow will deflect around the surface, others will impact it. I think it's intuitive that a greater proportion of the larger droplets will hit the aerofoil than the smaller droplets, because of the greater momentum of the droplets.
Since there are only two dimensions of interest, the radius of the droplet and the radius of curvature of the leading edge of the aerofoil, that also provides the scaling rule: the higher the ratio of droplet-radius/aerofoil-radius, the more rapidly a given shape of ice will accumulate.
Thus if you keep the droplet radius the same and decrease the aerofoil-radius, again a given shape will accumulate faster. Of course there's actually less mass of ice, because it takes less ice to make the same shape on the smaller aerofoil.