The Neuspeed Konis are shorter than stock and are revalved from the typical Koni damping to be stiffer. So yeah, they'll ride pretty stiff and are the source of your bumpiness. The Prokits are not a very stiff spring at all.

If you want to soften up the ride you can go for a softer shock like plain Koni Yellows or if you want a bit softer, Koni Reds. That would be cheaper than buying an entire set of coilovers.