Mike, grass carp are an easy sell for hatcheries but be sure they're right for you. They will eat almost anything before they eat algae, and if you have a lot of stuff growing on the bottom will rip it out and contribute to the murk. They will also come up out of the water, I swear, and pull plants (they really love elephant ears) off the bank.
As to the cloudiness, if it is pea-soup green, perhaps someone here can advise you on fertilization of the pond; I don't understand the process fully, but I have a vague awareness that causing a massive algae bloom can lead to clarification as nutrients are absorbed. One way to reduce algae adn bottom-growing stuff, add some bluing agent if you don't mind the color change (a little goes a long way, though). It alters the light wavelength and reduces growth.
For filamentous algae, which may or may not be the stuff growing off the bottom, chelated copper sulfate products like Cutrine Plus do a great job of pushing it back. You can easily tell by grabbing some if it is algae or plants; grass carp will be more effective if it is the latter.
Also, based on my experience, a newly-filled pond can have clay ionically suspended in it for which you can aerate until the cows come home without making a difference; a test I learned from Cecil on another board is to stand a big jar of the water for a couple of days and see if it stays cloudy. If the water has susupended clay, it's an easy fix with aluminum sulfate powder dissolved and broadcast; made a big difference for us.
24/7 aeration is awfully expensive, and it doesn't sound like lack of 02 is your problem.
