There is some problems about this model.
The first problem is why The pressure is not equal everywhere. Actually there is a solve but I was wating for defender of this theory defend it. I'm adding my own solution because I have not found a valid answer yet.
If you haven't found a valid answer how do you know there is a solution?
I assume you mean in the FE model, so a RE answer with gravity would be ignored?
Example:
If the doom has a radius more 3 times than land level;
But you have your dome touching land level.
Also, it seems you completely misunderstand how pressure works.
It doesn't matter what the shape is, the fluid is hydrostatic, and large areas outside doesn't magically make the inner areas higher pressure.
So the Weight of the land level of an object is 9 times weight of doom level.
Are you trying to discuss weight, which has nothing to do with air pressure (unless you mean the weight of the air), or air pressure?