Get a clear extension for your sewer pipe. After emptying the black tank connect a hose to the flush connection and let the water run for a few minutes. (I leave the hose connected if we will be in one place several days). You will most likely see additional solids coming out when the flush starts running. I typically close my black tank valve while the flush is running, let the flush run for 2-3 minutes to build up some water in the tank, then open the black tank valve, and let it dump. Then repeat a time or two until I see little or no more solids coming out. The extra clean water accumulating in the bottom each time seems to flush out extra solids.
Just do not forget and leave the flush running very long with the valve closed.