I think the first thing to do is figure out what the particles are - its not single cell algae because that wouldn't separate and settle out of the water. Do you have a pine tree that sheds pollen which is a fine brownish powder that pine trees drop in early-mid spring? Its the color of your brown water which made me think that's what it might be! Another clue is - is the color same as the fish food you are feeding.
My guess based on the foam on the water (and my own past experience) is that plant and other organic debris may be going thru the pump and then as it breaks down into ever finer particles that cant be caught by usual filter - it can affect water quality.- I have heard this referred to as (excuse the crude expression) fish poop puree. The foam may indicate dissolved organic compounds which signal worsening conditions - how is your water testing, any ammonia/nitrites?
Either that or someone was spawning
My strategy was to use the fine filtration as needed - esp in Spring when the dang tree was dropping the pollen - and Im afraid there was no getting away from having change & rinse the pads several times a day. Later on after pollen drop, I could go days without having to tend to it and then remove fine pad entirely. I switched to a solids handling pump so that the poop and plant debris was less likely to break down and it collected more effectively in the Biosteps 10 filter (external filter with 8 layers of matala + the fine filter pad when needed).
Im definitely interested in what other people have to say though, cos it wasn't an entirely head-ache free solution. The fine pads I got from Dr Foster and Smith and where much more affordable and effective than that dang quilt batting from Wallmart (that stuff aint cheap) and also had the benefit of being washable and reuseable throughout an entire summer.
However Ive not found a new source for it since F&S is no more and the outfit that took it over is pretty lame in the pond department. Will let you know if I find anything! They also sold a less fine, but pretty good polyester filter - like quilt batting but sturdier and reuseable.