If I understand the issue correctly... You can dump your black but you cannot get the rinse out nozzles on the interior of the tank to spray water into the tank. Try filling with fresh water and some detergent by using a hose down the toilet, use hot water if available. Let it set for a while and then dump the tank and see if your nozzles will work then.
I use a wand as the previous poster mentioned and that works for me. You do need some Clorox water and a rag available to clean off the hose if you want to use it again for anything else.
BTW how is the lake level. I was planning on fishing some in a week or so. I live in Las Cruces.