Another "out of the box" idea. Drive the RV to a very cold below freezing area, let the black tank turn into a poopcycle, remove the defective valve and replace it then drive to a warm climate letting the tank thaw out. Then dump as you normally do (still talking about the black tank here)
Another OOTB idea, drive up a really really steep hill so the valve is higher than the tank, remove and replace the valve and drive down the other side to a dump station dumping as you normally do!
Ok, Ok, # 2 is still probably the best idea (talking about post #2 here people)