Hi, Steve - Now with that photo, I can see that the particles are actually in/under the paint surface. By the way, it was a very good decision to test on such as the spoon, rather than a model.
First your question about filtering, I filter when pouring mixed paint in the AB cup. But there are several prior steps to consider.
1) Paint in the bottle. That is usually dependably in good condition when freshly opened, but solids will have settled. At first use I always give it a thorough stir, making sure the stick moves completely around the bottom, gathering up all of the settled solids. That will appear as a ball of gunk at the bottom of the stick, continue stirring until that wad has been blended with the rest of the bottles ingredients, and is a consistently smooth liquid. Then I use a Badger stirring blender, (any will work that can fit in the bottle.) That may sound like overkill, but it really does make for an even more thorough blending of the paint, well worth the time.
2) I absolutely NEVER shake it to mix, at any point in the life of the bottle. That only makes for a messy cap interior and bottle threads, plus paint on the insides of the bottle dry and can result in flakey bits that get stirred into the paint at next use. That would be a time when filtering of the paint from the bottle would be needed, but as you said, it's pretty thick stuff and I think a good bit would be wasted. Stirring is the better way for me to prepare the paint for use.
3) I don't pour the stirred paint out of the bottle, I use pipettes for drawing it out of the bottle, for blending with thinners and additional agents. That keeps the bottle and remaining paint in like new shape, for continued use.
4) Prior to adding paint to the AB cup, I always run at least one full cup of the SAME thinner added to the paint through the AB at high pressure, 30 psi or more if possible, two rinses even better.
5) Ensuring the filter I'll use is clear of any foreign material, then I add the spray ready paint to the AB cup.
After use AB cleaning, (in my opinion,) involves much more than a simple spray rinse of the brush. Any dried paint residue left behind in the AB can break loose at next use, then contaminate the spray mixture as it leaves the AB.
When through spraying I run a thinner rinse batch through the cup and AB, remove the cup then swab it out with Q-tips and thinner. Then I invert the AB, (nozzle end facing down,) pipette thinner into the cup intake port, then press the trigger and spray that through the brush, repeated a few times. By then the AB is FAIRLY well cleaned, but not completely..
I have a 155 Anthem among several others, and can describe some of the interior spots that do require physical cleaning with implements. like cotton swabs, interdental brushes, even toothpicks enter into my regimen. First is the 155's cup intake port, that needs a good swabbing with a cotton bud soaked with appropriate thinner. I insert the swab, then pipette some thinner into it, swirl it around and keep at it until the port is fully clean.
With the AB disassembled I use an interdental brush, enter the front of the body, then pipette thinner into the intake port, (still facing down.) Run the interdental brush around, back and forth, that will agitate paint residue and put it in solution with the thinner, repeat as required, now the body is clean.
Cleaning of the spray nozzle, head and needle is straight forward, easy to see what needs cleaning and how to get to it. So, the contaminates you see in your test sprays, could come from several sources, paint bottle, airbrush residue, cleaning equipment, etc. For that reason I avoid using paper towels, but there are lint free towels available at a still affordable cost.
I hope you get the situation resolved, likely it's something rather simple causing it, best of luck with it. The first place to start would be a thorough cleaning of the AB, then try some fresh paint. I always remind myself that foreign bits come from several different sources, I try to eliminate them by methodical steps along the way. I get P.O.'d easily when I do screw something up, (and knew better.)
Patrick