The "fines" I assume is clay or silt. Clay and silt is in the 1 micron range. For comparison a single cell algae is in the 25 micron range and bacteria in the 1/4 to 1/2 micron range. So it depends on the type of clay you have and how much movement in there is in the water. Stirred up clay will never settle. Algae canl chunk onto it over time and together settle but algae can have trouble growing in clay filled water.
Clay is way too fine to filter with quilt batting. Some will of course settle in the batting and anything else but it won't clear the water. You'd have to use a sub 1 micron drinking water filter, and it would take a lot of them, like hundreds of dollars.
UV filters have no effect on clay. Clay is a mineral. UV only effects living things, algae, bacteria, Grandma, etc... The number of gallons in the pond also has no effect on clay settling. Depth has an indirect effect if seeing the bottom is the goal.
Your poultry fence filter is for the ammonia conversion cycle and will not remove clay. Some may settle in the drum like the batting but no more than anywhere else.
If you dip the glass into the pond it will also appear clear. There's no difference in the water coming out of the falls and the water in the pond as far as clay goes.
Muddy water is kind of normal in new ponds. A lot of dirt tracked into the pond during the build, on rocks, etc... If this mud did run into the pond from rain, heavy or not, that issue would have to be corrected first before any clearing can take place long term.
So at start up a pond it is filled a bit, washed down, and the muddy water pumped out. That is repeated until basically clear. If you want fast results this is the only method that works no matter where the mud came from.
Or you can wait and see what happens. Maybe it will settle enough for your taste. Goldfish and Koi will actually like the clay better than clear but generally they don't get a vote.