So could the solution really be as easy as suggesting my hubby have a pee party? He hasn't been able to do that since the last AP system we cycled...he would be thrilled!
I've killed Duckweed Sylvia by adding too much nitrogen fertilizer to the water. It seems to grow well if there is no visible surface disturbance of the water and the water is stagnant or slightly brackish. I have seen it die in full sunlight with too much heat. Grows fine is dappled light. Maybe your black bins get too hot?
"Growth conditions The natural habitat of duckweed is floating freely on the surface of fresh or brackish water sheltered from wind and wave action by surrounding vegetation. The most favorable circumstance is water with decaying organic material to provide duckweed with a steady supply of growth nutrients and trace elements. A dense cover of duckweed shuts out light and inhibits competing submerged aquatic plants, including algae."
More info : http://www.p2pays.org/ref/09/08875.htm