About a week ago I took out my gravel substrate of my already established and stocked tank 55 gal and replaced it with a plant substrate called SoilMaster Select, made by Pro's Choice (which is owned by OilDri IIRC).
IT WAS A MESS! It was really bad. I took a 3 gallon bucket, filled it a third w/ the substrate, and in my tub I filled it while mixing, mixed a while longer then dumped it out. I repeated this so I did it three times total for each batch. The first couple of batches I rinsed a lot more but stopped noticing any increase in clarity. I think the mere mixing of it was making it dusty so I stopped at 3 times rinsed.
I guess I did about 10 batches before all 50lbs was in and it was sooo cloudy I couldnt see halfway into the tank. I was really worreid about all of my fish b/c it was sooooo thick w/ dust. I did about a 50% PWC that night and it helped.
By morning, the tank was crystal clear until I did some more "construction" lol. It was never as bad as it was the first time though. Just getting it rinsed and in is the major issue. Once that is done, and the particles have a chance to settle, it should never be that bad again.
This wasn't laterite, which is cloudier, but the theory works the same.
I would definitely run your filter, but just clean it like once a day for two or three days. It really helps catching all those suspended particles. It will get "full" w/ debris quickly, but hey, cloudyness caught in your filter and rinsed down the sink beats cloudiness still in your tank right?
I'd suggest keep rinsing out your gunked up filters, let the water settle and over time the cloudiness will go away, and keep up the PWC's to replace those gallons of cloudy water with gallons of (dechlorinated of course) crystal clear water.