How you put the sand in will greatly affect how much cloudiness there is IMO. If you just dump it into the water, which allows all the water to flow through it as it sinks to bottom, you will get lots of suspended sediment (silt, clay). If you somehow shield it from this, like say using a cup to bring it from top of water to the bottom, then slowly pouring it onto bottom, then yes, you won't get a lot of cloudiness. It really isn't rocket science. I have been assuming one extreme the whole time--you just flat dump the stuff in. There are of course better ways of doing it that will minimize suspended sediment. The best way to it, if one is that motivated, is to suck out all the water from the tank, then put the sand into the tank, rocks on top, a layer of saran wrap on top of the whole thing, then slowly add the water into the tank. When done, remove saran wrap.
BT, could you please tell me what other minerals besides arragonite you could be washing away? Really, I may be missing something. And also, I assume since you say rinsing would be washing it away, that these minerals are only contained in the dust, not in the arragonite sand grains themselves, which would be released at a later time in the anerobic part of the DSB.
kris