Thank you all for your replies.

I will have to do some more research. There really is no place on my property to place the massive amounts of muck. I would like to keep it since I think it could be turned into some good soil once it dries but I doubt I, nor my neighbors would be able to handle the smell until it dries. The only alternative is having it hauled away, which would be costly.

I took a kayak out on the pond for the first time this spring and there are tons of small fish. Most of these are carp like. However I did see some bluegill like fish (round bodies rather than the slim longer small carp). I also see a bunch of fish jumping on the surface. Do small carp jump? There are also some very large monsters 30+ lbs by my estimates. I haven't really seen the carp muddying up the waters though.

If I would forgo the dredging or decreasing the size, would getting rid of the carp allow for some other species to be introduced even though the water wouldn't be very deep? Or will the problem of leaf debris only get worse as time goes on? It stays under 65 degrees even in the summer and never fully freezes over during winter.