Wait, Wait, Wait!
Here is what you do. So, pumps clean all water that passes through them, and you kind of need them not to do that to get contaminated mist right? Well, why not just pump the water up to the same z-level as where it would fall to generate mist, and then have it pass through a tile covered in the contaminants? It should carry them with it, as it falls to the next Z level and becomes mist, thus enabling us to create our true Dwarven Auschwitz. You could even recycle the water, because the original tile would still be contaminated.
Drawing:
XX_v
XXww I I_v
_______________
_ = floor
XX = screw pump
v = floor gate
I = wall
w = water
The first floor, the upper most that is, would need to be contaminated. The water would flow through the contaminated tile an then down the two floor grates to the bottom floor, where it would then flow towards the back and be sucked up by the screw pump.
You might not need floor grates, but I think that might be necessary to get things to spread through it.
You could use this setup, or a similar setup so long as you just make sure to contaminate things after you have pumped the water, to cover an alternative entrance to your fort with forgotten beast extract.