Hi and welcome! I haven't read every post in this thread but I looked at your pictures and read your concerns.
It sounds like your set up is similar to mine, so I'll try and provide some tips based on the set up you have.
I net out the bottom of my pond once in the spring and again in the fall, sometimes Ill give it a third netting out in mid summer if I feel ambitious. I use a pool net and dump the "gunk" into a wheel barrel, take it back to the garden and dump it in the soil.
I have two skippy filters and a small bog. Two pumps sit in the pond. The hoses to the skippies should take the water into the bottom of the skippy in a circular direction. The water should spin in a circle up through the filter media then out the top into the pond.
I have clean out valves at the bottom of the tanks so I can flush the gunk out of the bottom when needed. This is the only cleaning I do to mine. The tanks come with a drain. I simply added a fitting and ball valve to the drain. Then I hook a hose up to the drain and turn the valve. The gunk flushes out through the hose to whichever flower beds gets lucky that day.
I do wonder about the one tank flowing into the second tank. It seems if the water enters and exits the top of the second tank you aren't getting much filtration from it. You want the water to enter in the bottom then force its way up through the media and out the top.
This year I drilled a small hole in the pvc that takes the water into the bottom of the skippies and ran air hoses from a small air pump. I actually think that made a huge difference in water clarity this year though I wasn't really having issues to begin with. Oxygen in the filter media helps promote the growth of beneficial bacteria.
If I were you, I'd start by scooping out the bottom of the pond, and flushing the gunk out of the tanks. I'd probably do this several times since each time you will stir stuff up and it will settle again. Maybe 2-3 times to get it fairly clean. I'd also do small water changes frequently. After that I'd watch your system to see if changes should be made.
Changes I might consider is putting a separate hose to each tank (you can either get a splitter or a second pump) and making sure the water enters through through the bottom.
I'd inspect the filter media to see if maybe its old and has degraded over time. Depending on the media that can happen.
I'd pump oxygen into the bottom of the tanks.
I'd look at the amount and size of koi and see if it's possibly over stocked.
Maintenance, I'd do small weekly water changes and larger water changes in the spring and fall when I scoop out the bottom. That's all I do since when I do the water changes it flushes the skippies. I added a picture below for you to see my set up. The water from my skippies overflows out the top into the small bog. The small bog also has water pumped under the gravel, then all the water flows down the waterfall and into the pond. I built a deck over my skippies with access panels from the sides and top to open and close valves when needed.
I have 9 koi in about 5000 gallons with this filtration. I also have about 15 comets in there.
View attachment 83408 View attachment 83410
View attachment 83409
Edit: I'll add before I added the drain to my skippies I cleaned them with a shop vac. I let as much water drain from them as possible using a siphon, then stuck the shop vac in the bottom to get the gunk. This was not ideal and messy and annoying so I added the flush out valves. Now I simply open them and leave every thing running. Let them drain about 10% of the water volume of the pond through the drain valves and set the garden hose in the bog to add the 10% back.
Second edit:
Also I noted that you said you could see gunk in the top of the tanks looking down. I can as well as the gunk coats the filter media. that doesn't necessarily mean the tank is filled solid with gunk up to that level. But either way with the smell of the tanks I'd definitely clean the gunk out.
