Isn’t there a way you can put a sump pump in there to pump out the silt but have a way for the water to drain back in? Don’t know how expensive that would be but those dredges they have on the beach replenishment projects at the shore sure do move a lot of sand.
Dredging in a grid pattern off a barge is an option. Costly and you need lots of "up hill" land so water will drain back. Hauling it off the property opens up the government floodgates to soil tests bla bla bla… to go to a land fill. I'm not dumping toxic waste but my drain field I collect rain and other surface water is hundreds and hundreds surrounding farms, woods and country side. Lowering the lake and digging and pushing silt out seems to be cheaper route. I have often thought that a private sale of the diggings to a larger green house might make a few bucks to offset the cost of the project. The black muck most be incredibly rich. When the lake is dropped and bottom areas expose and dry, grass and weeds pop up and grow twice as fast and those on shore.