Many times, aeration can cure some of the problems such as muck build up on the bottom.
Most likely, you've got at least a foot or more of muck on the bottom.
Like others have said, in many states, if one's property borders up against a pond, then they have rights to use the entire pond. Also agree to try and get formal agreements in place.
You also have the option to have a diverse fishery.
My main pond is similar in size and has at least 10 species in it. You never know what you're going to have on the end of your line.
Grass carp seem like they'll be needed too.