Clearing the black-water dump valve

That's a good solution and should work every time. Another technique is to use the grey tank to back flush the black valve. Some people install a third gate valve to do this, but I just hold the stinky slinky up above the level of the tanks and open the grey valve and let the tank levels equalize. Once flow has stopped between tanks, I close the grey valve and drop the hose. You can do this a few times, but once is usually enough. Finish up by draining the grey tank.