Let's not forget that we are dealing with an earth-bottom pond.
The water will never be clear, nor should it be. 18" visibility is considered good in the typical earth-bottom pond. With the addition of bottom feeding fish such as Koi or catfish, visibility will be considerably less.
By nature, a healthy earth-bottom pond will support sizable population of both benthic (bottom dwelling) and planktonic (floating) microorgainism...algal and animal. This rich diversity of life, especially planktonic, in sufficient numbers greatly affect the turbidity (clarity) of the water column. Bottom feeding fish add to this turbidity by stirring up very small particles of silt and detritus that remain in suspension for a considerable period of time.
Filtration will not improve the clarity of the water. A pump is not necessary. A diffuser or bottom-fed fountain will create all of the water movement needed.
Since it appears that you have considerable aquatic plantings, a 'bog' filter would offer no advantages, but would prove to be just one more maintenance item as, over time, it would fill with the suspended silt and require complete dismantling and cleaning.
In truth, what you are experiencing is a mature earth-bottom aquatic eco-system.
One thing that I could find no mention of in this thread was...... feeding the fish.
If you are feeding them, stop. The pond is brimming with all of the natural food the they require. Feeding will only increase the organic load of the pond.
In conclusion, you appear to have a fairly healthy earth-bottom pond.