I don't know if this helps or not, but I set up my 5.5g with aquasoil powder, and it kept a brown tint to it for a month, and it never cleared up. The soil wasn't especially dusty or breaking up or anything, it was just badly tinting the water.
I really wanted to use AS, so I gave it the benefit of the doubt that I just had a bad batch. So after about a month of wait and see hoping it would clear, I took everything out and put in a new bag of AS powder (type II, not sure what type the first bag was actually, but I believe it was type II). The water has been clear with the new bag since day one, so I'm convinced I really did just have a bad bag of soil.
So... maybe your soil is leaching tannins and the tank isn't actually dusty. Maybe put a little of the soil in a cup without any circulation in a closet, and see if the water stays clear.