Skippy is a bio filter for removing ammonia if you have more fish than than the pond alone can handle. When the pads get coated with muck it covers the bacteria and they die. Not to worry, the bacteria are happy enough living elsewhere in the pond so I'd assume ammonia is zero.
The single cell green algae is in the 25 micron range. Here's pantyhose and a much more dense nylon cloth under a microscope. The right side picture shows a few bits of trapped single cell algae. But most of the space is wide open. Those pads in the skippy are way-way more porous. Muck settles on the pads just as it settles on the pond bottom. The pond is much more effective because the "flow rate" is near zero. Hard to match that in a skippy. Vacuum the muck off the bottom of the pond and you'll get way more out of the pond than a skippy will ever do.
My point is those pads in the skippy do little to produce clear water. There's no logical reason to think they would.
Stuff that settles isn't the stuff making the water unclear. Much finer stuff is in play.
There is a bacteria, separate from the ammonia converters, that do produce an enzyme that breaks the walls of single cell algae and kills it. But that bacteria isn't well understood and algae have their own defenses too. My personal guess is the algae have to start dying first from some other cause, before the bacteria can grow to enough numbers to make a difference.
Another killer of single algae is string algae. It can produce a chemical to kill the single cell algae, called allelopathy. The single cell algae also have weapons against string algae. But in general the string algae seems to win more. Adding even a small amount of string algae can sometimes clear a pond in a couple of days. Then again, somethimes it's the string algae that dies.
When people say adding plants to clear a pond it's the hitch hiking string algae that should get the credit. But that's human nature. "I added plants to clear the pond, the pond cleared, so it must have been the plants." Of course there's no logic to plants removing enough nutrients to starve single cell algae. They need little and are better at getting it, being that they're throughout the water column. If you measure the nutrients in a green pond and then after the pond clears there will be of course a much higher level in the clear pond since the dead algae release nutrients back into the water. Adding a potted plant to a pond adds way more nutrients than they remove.
Norm Meck did some experiments years ago that showed water from a clear pond killed green water algae.
http://users.vcnet.com/rrenshaw/GRENH2O.html
UV lights are very effective against single cell algae. You already have one installed, the sun. The UV filters are just way more powerful in a small space. But the sun will have the same effect over a longer period. Single cell algae will form clumps, called colonies. That is when pantyhose type filters can start being effective. The colonies less buoyant and more likely to settle.
So over time there is a chance something will kill the single cell algae and the pond will clear. You'll still have some of course, and the dead algae will be suspended in the water column making it less than perfectly clear. Fabric filters are very effective at that point.
The test should be if a filter is collecting muck it's a mechanical filter. To be effective mechanical filters have to be cleaned often. Once a day, every couple of days...often. Good bacteria won't grow on media that is always getting covered.
No muck collecting and you have a bio filter, a home for all kinds of bacteria. One of the best bio filters for hobbyists I think is a stream. Lots of surface area that is always being cleaned free of muck allowing for bacteria to grow. They're trouble free. Back in the day when I cleaned ponds I don't think I ever found a "bio filter" that wasn't clogged with muck. Completely worthless in all regards. But you can't tell ponders that. They want to see that box "filtering". When the pond clears on its own the yell "Eureka!", the filter worked. String algae and bacteria never get the credit.