The answer is this: You will need to cover the item you don't want to heat with a conducting material, creating a so called Faraday's cage, which is connected to an earth potential equal to the potential of the metal casing of the microwave oven.
The reason for this is threefold: The covering material needs to be a conductor, because conductors have the property that free charges can move free without significant resistance inside it. Because of this, the electric field inside the conductor is zero, for elsewise charges would move due to the electric field. But they move themselves in such a position that they cancel out the fiel again. Now, because the electric field inside the conductor material is zero, is also has to be zero in cavities of the conductor. For if it would not be zero inside the conductor, one could move electrons through a loop partially through the cavity, and partially through the conductor. The path integral through this closed loop would then be non zero. In onther words, one could generate energy without costs, obviously in contradiction to the law of conservation of energy. Therefore, wrapping an item in conducting material creates a so called Faraday's cage, whereby the electric field through the wrapped item is zero.
Now this is what we want, because the microwave oven heats items with the use of electric field waves. So, shielding the item off from electric fields, also shields it from heating.
However, charges inside the conductor start moving because of the electric field waves. This can create a potential difference with the shielding material of the casing of the microwave oven. It is because of this difference that arcing could occur. That is why you will also need te connect the conductive wrapping to the earth potential of the metal casing.
I think this question is more about the engineering (and economics) of manufacturing microwave ovens.
The standing wave pattern can create hot and cool spots in larger food items that are not moving inside the oven. The rotating plate is sufficient to move the food around so that most of the food is not stuck in a node that creates large temperature differences. Food directly along the rotation axis moves very little, but it's only a small fraction. In addition, this region is more likely to be on the interior where the direct heating effects are reduced and temperatures may have more of a chance to equalize after heating.
Moving the entire assembly in one direction would accomplish almost the same (admittedly it would eliminate the static axis) , but would require a more complex mechanism. Also any translation would reduce the usable volume inside the oven. A plate that shoved a reheating chicken onto one side of the oven might not be appreciated.
So it becomes a trade-off between more expensive ovens and the chance that small portions of the food on the rotation axis might not be as uniform as other areas. It seems that most users perceive the microwave oven as a non-precision device and are not willing to pay significantly more for small improvements in cooking ability.
Best Answer
Good question. The rate of temperature increase scales as the power absorbed by the food divided by mass of the food. So to understand your question, you need to understand how power is absorbed.
There is a finite amount of power in the microwaves being produced. These microwaves bounce around in the metal cage where you put your food, until they come into contact with the food. (Well, some of them will get absorbed in the metal by imperfect reflection, but let's ignore that at first.) Once they get absorbed by the food, they turn into heat. Because they bounce around until they hit some food, the efficiency of a microwave is pretty high, in the sense that most of the power generated in the form of microwaves goes into heating the food, regardless of how much food you have.
So, at lowest-order, increasing the mass will increase the amount of water, but won't increase the amount of power being absorbed by the food. But now, that thing about absorption by the metal comes in. The power absorption will be slightly greater with a lot of food, since the food will be more likely to absorb the microwave before it gets absorbed by the metal. This is a lower-order effect, but it's there.
Of course, then the issue of skin depth comes in. Microwaves only penetrate a certain distance into the food. (Of order an inch, depending on the food.) So increasing the mass isn't really what you want; you want to increase the mass that's within the skin depth. For example, a wide dish of water that's one inch deep will absorb better than a jug of water with the same volume. This is why you want to split apart chicken breasts when defrosting them, for example.
To answer your question, then, the more food you put in, the more efficiently your food will capture the power being produced by the microwave oven. So you will capture the microwave's power better, but you will still heat slower because you have more mass. But this is not a dominant effect, and you might be better off redistributing your food to maximize the surface area.