Thanks for the advice, but unfortunately, the problem is not with my black tank. The black tank is emptying very well and is holding the usual amount of waste. Also, I have a built-in flush mechanism I can use with the black tank. I think I was not very clear about what was happening, so here is more explanation and what my thinking is:
The problem seems to be with the outlet of the grey tank, not the tank itself. In other words, there is liquid in the tank, but it will not empty, so I think there is either something stuck in the outlet or the outlet itself is broken somehow. I have already done all of the things to break up anything in drains to the grey tank or the grey tank itself, including more than two bottles of drain opening chemicals and even boiling water. I also dumped an entire bottle of dish detergent down the drains in case it was a grease buildup, but that did not help either. I also have gone through a bottle of enzyme product that is supposed to clean our grease and hair. Obviously, water is going into the tank, but it is not coming out and is making the tank fill up too quickly.
Also, this happened very suddenly, not over a long period of time it would take to fill the grey tank with something blocking the tanks. That makes me believe that the problem is not due to a lot of stuff that has built up in the grey tank.
Also, the problem is not in any of the P-traps for the shower, kitchen sink, and bathroom sink because if I add water to any of these, water starts to fill up the shower pan.
My two tanks share an outlet where I attach the sewage dump hose. About 3-4" above the bottom opening, the wide black tank plastic pipe is joined in a Y shape by the smaller grey tank plastic pipe. Based on my eliminating problems in the p-traps or anything inside the RV, the problem has to be in the grey tank pipe or the grey tank release handle. That is why I tried to shoot water with the hose from the bottom up into the grey tank with the release handle open.
I will be able to tell tonight and tomorrow morning if that helped unclog something.
I may be completely off-base on this, but my next step is to try to find a company that will flush my tank. They would have something that could flush further into the outlet, and possibly be able to put a camera in there to see if I am off-base with my analysis of all of this.
Anyway, thanks for your help.