+1 to most of the comments here. Flexible hose on the outlet, rubber fittings and other mounting insulation, and an accumulator before you replace the pump itself. If that doesn't work, all of the things you added to the old pump will also serve to make the new pump as quiet as possible.
It may be that DW demands a pump replacement regardless of the improvement you see (well, hear) from the other interventions. In that case, you will have ventured into the hinterlands, where our knowledge cannot help you, and your only hope is for a straight road and a merciful god