Duckweed is a viable option, but I don't think it should be the only one. Worm farms (vermicomposting bins), black fly larvae farms, bug zappers, and duckweed could be combined for a diverse and nutritious diet. Some species of perch, like the Jade Perch, are omnivores and can be fed from the aquaponics garden. A grow bed filled with could be harvested in 3-4 weeks, and if combined with the previously mentioned dietary options, the aquaponics system comes closer to being completely closed loop.
At this point, one of the last remaining input problems is the energy need of the system. A self-regenerative off-the-grid stand alone power system would reduce the cost of outputs (cost being the cost of producing the outputs relative to inputs) to almost zero. I've been fooling around with drawings incorporating Tesla turbines (one in the form of a Tesla water pump) hooked up to a synchronous AC induction generator. The electricity produced from the generator gets routed through the system by a charge controller to maintain a consistent load on the generator, with batteries added for energy storage. The system pushes excess load to "dump" locations such as water heaters and air heaters (both of which could be used to maintain atmospheric and fish tank temperatures in the greenhouse). This design is far from a finished product, however.
Hope this helps.