Is there anything I can put into a pond to make suspended sediment condense and settle out?

I have a small 1000 gallon, unlined pond that is about 7 ft deep. The soil is clay and I threw in about 50 pounds of additional bentonite clay to help seal it. I have an air bubbler running 24/7 to keep the water aerated and the fish happy.
There is one problem. The water is mirky. I can only see about 2 to 3 inches down. I considered getting a filter but the cost is outrageous, $300 to $400, and it requires a pump for an additional $200 and it needs maintenance. But it will theoretically clear up the water perfectly. The system is overkill.
I don’t need the water to be crystal clear. I just want to be able to see down a foot or two.
As an experiment I scooped up some water in a jar and let it stand on a window sill. In about 3–4 days the particles settled out and the water went from cloudy to clear so I know it is possible to have clean water.
Is there some magic chemical that I can add to the pond that will cause the fine clay colloid particles to condense and settle out? I would prefer if it did not kill fish as there are 29 of them happily swimming out of sight.
I’m open to other suggestions.