I think filtration here is a big part of the issue. First thing is there are a good number of manufacturers selling tumbler systems and from my experience they provide the equipment, provide a poorly written description of its operation, and pretty much leave the proud new owners of the equipment on their own.
I do not understand why, after using the filter to filter the dissolved alloy in the tumbler, they feel there is a need for an in line filter. You either filter properly or you don't. On thinking about this, and going back over the photo's, and what I know first hand about other tumbler systems, there are a few things amiss.
In this photo provided by the OP, the grid on the bottom of the filter has some rather large openings.
The OP has said they use a reusable fabric filter on this filter. He did say the filter is held in place with a gasket so I assume nothing leaks around the filter. But from what I know about these filters, if the openings are too large, as these are, there is a necessity to put a fabric over the grid to prevent any filter sheets from sucking into the holes. I believe the screening the OP is using is intended to support the proper filter papers placed on top of the reusable screen. And by not using any filter media other than that screen, silver chlorides will definitely pass through the filter. What is the mesh size of this reusable screen can Gold Refinery provide us with that information, and possibly a close up photo of the screen? If the filter is working as intended it should not require a downstream spiral wound cylindrical filter.
Secondly, they drop the gold in one of the tanks, again filter it, and then store it in another tank to, as Gold Refinery put it
The first tank is for precipitation of gold.
Then the mother solution is transferred to the second tank after the gold is filtered (here the gold remains on the filter).
It stays there overnight and then filtered into the third tank (here the sludge contains copper and the rest of the gold left over from the previous stage).
Again, if the filtration is proper, the gold precipitates should be in the filter, not beyond. A well designed refining plant puts all of your values (within reason) in one place and shouldn't leave the refiner chasing all over the process equipment looking for lost values. Gold Refinery, a close up photo of the grid on the filter and of the reusable screen you place on top, I think this is an issue we need to correct.
A tube with air flow is used manually to completely dissolve the solution and mix it.
Bubbling air is not an effective mixer with something as dense as gold. It's great to move solutions but when precipitating gold there is something that happens when you drop a lot of gold that most do not realize. When you have the air bubbling and start dropping your gold, as the gold drops, it is blanketing the bottom and actually remaining surrounded by gold in solution that becomes trapped under a few inches of precipitated gold mud. Since a column of air bubbles will not effectively lift the gold off the bottom, the solution mixed and trapped under the precipitated gold can not react. You finish adding your precipitant, test with stannous, and assume all of the gold is dropped. Except there is gold in the solution trapped by the gold sponge that has not been properly exposed to the chemistry you are using. Remember we discussed just how much gold a small quantity of aqua regia can hold, this can be significant in your case.
The fix to this is to physically use a wide blade paddle to physically move the gold sponge you have precipitated and allow that solution to also react and drop its gold. Most systems have a large blade mixing motor to assure good movement of the gold as it drops and keep it moving to avoid this issue. Your air bubbler will not accomplish this.
When you transfer to the next tank, that solution which still has gold in solution, reacts with the chemistry and drops out. It can pass through a filter when it is dissolved but will drop in the solution it is mixed with in the next tank. Possibly that is why there is a second tank. To use an a
American phrase, that is Mickey Mouse! To fix it, agitate properly to assure complete precipitation and filter it properly and it will all be where you expect it, in the filter.
Everything we have touched on thus far reflect on the operation of the physical equipment, not your choice of chemistry. Send photos of the grid and the screen to help figure this out.
I did not understand what you meant about our wrong analysis with XRF.
XRF is often mistaken on sludges or powders and without proper sample preparation and the proper algorithm running on the software, the answer spit out by the same XRF you used to analyze the karat scrap is not to be believed.