Here in Texas, the State will provide all of the information needed to make this type of pond healthy. In fact, they will even provide the fish in some cases. I have a friend who is going through this now.
It's easiest to work on an empty pond as it is being filled, but I'm sure that a full pond can be reclaimed with a little more effort.
Completely different climate I know, but my grandfather has a healthy pond in Texas which is at least 12' deep. With the proper plants and conditions, the oxygen will circulate even to the bottom without mechanical circulation according to the literature he has.
Native fish would probably be the best way to go, but if carp are native to your area, then koi should function fine as a part of your pond ecosystem. Here, carp and humpback catfish will be present in any healthy pond. The birds carry their eggs. Bass must be added to control catfish populations.
-Shay