I had some material, that had some small gold foils and tiny flakes of gold, mixed in with many other metal powders, much like some of the materials you are centrifuging, just for the fun of it I thought I would try and pan a small sample, what I noticed is the material would not separate by panning very well at all, the fine gold powders and foils are just moved along by the other material, the gold is also so fine it will float around in the water, sometimes almost easier than some of the less denser metal powders.
I do not know if the centrifuge, would have the same trouble as I seen in the pan, but I think it possibly could have, I think it would be interesting to make a small controlled experiment, taking some very fine gold foils, powders and so on, and weigh them, mix them with a little of your sludge material, in the consistency, you normally have, then run it through the centrifuge, and see what you recover back, also testing the solution that floated out of the pot, who knows floating the gold with froth floatation and centrifuging at the same time (probably at a lower speed may also prove to be a way to recover).
P.S. the screen in the skillet, I really like that tip, on second look that may just be a plastic strainer that looked like a skillet to me in your picture, I have been having a lot of trouble drying material for incineration, taking a long time at low heat to dry out the liquid in a corning dish, as the material will bubble and spit if heat is raised too high to fast, it can take all day on warm before it is dry enough to raise the heat, the screen holding the majority of the material off of the bottom may just be an answer, this way the liquids below could be raised to a higher temperature, steaming through the material held above in the screen, any spitting would stay in the pot better, once more dry they could be crushed through the stainless steel screen to the bottom of the pan ready to raise the heat and incinerated.
