I think you would agree that perception is "subjective" by your definition: my seeing a red hat, for instance, does not mean that you see a red hat: it is solely my perception. Of course, given the same or similar conditions, we might have similar perceptions, just as we might assign similar meanings to, say, the sight of a car veering off toward a group of deaf students. But my perception is in my mind, and does not affect your perception in your mind, unless I communicate it to you in some way.The problem with that is perception is not solely in your mind at all (unless you do believe in the brain-in-a-vat theory). Indeed, if you perceived something that was only in your mind, that would be the definition of a delusion, wouldn't it?
The only way you can link perception and meaning is if you agree that objects have something that makes them meaningful in and of themselves. That is, meaning has to be objective in some way.
Consider it. We see a red hat. Even if the concept of "redness" is different for you than for me (that is, suppose that you see as the color "red" as what I see as the color "green") the fact remains that the object that we see exists and it exists in such a way that it absorbs all light except for that which we both perceive. That our perceptions are different is irrelevant here. After all, the object emits color X. The fact that your "red" is different from my "red" is irrelevant, because X itself is always labeled "red." The objective nature of X remains the same regardless of what we perceive.
But your idea of "meaning" is in no way similar at all. In atheism, objects do not exist with "meaning" attached to them in any way. There is no property "X" that conforms to "meaning" which we both perceive. Meaning is completely manufactured by you, and by you alone. Meaning totally exists within your subjective sphere and never shall depart it.
So your illustration is disanalogous.
I also find it interesting that you add: "unless I communicate it to you in some way." How can you communicate something that is completely subjective? Communication can only occur if you have ideas that transcend individuals, but that requires an objective sense for them. In the color example, the fact that X is objective allows us to communicate X to one another. We give X a specific label: "red." It doesn't matter how we perceive that, each of us labels our perception of X as "red" and therefore communication results.
In order to talk about meaning, you have to have an objective concept of meaning in place; but in your atheism, you've already said that meaning is itself completely subjective. It doesn't exist in the object, but in the "meaner." It is therefore impossible to communicate it.
Consider this: we can communicate colors because we link them to an objective fact. But suppose again that what I see as "red" you see as "green." This is a literal fact for the purposes of argument. But how do we communicate this to one another?
We cannot. I don't have access to your perception, so I can never compare it to what I perceive. All I have access to is what the object emits, and we both conventionally use the same label for that. So if our perceptions are different here, it is impossible for us to say they are different. I can never know that when you see color X that is labeled “red” you actually see what I call “green”, because I don’t have your perception.
In fact, the only way to determine that another's perceptions are actually different from ours is if they are unable to distinguish between the objective qualities of the object. For instance, my father is color-blind. He cannot see the color red at all. The problem for him arises not in the perceptual area, but instead in the objective area. That is, one object emits a color B and we call it "blue" and another emits the color P and we call it "purple." My father, who does not see the red in purple, says that B = P because to him both are "blue." We can tell this is wrong because we can see that B is NOT the same as P; there is a difference that he cannot see.
We know the problem not because we have access to his perceptions, but because we have access to the objects themselves. Thus, perception has an objective quality to it.
Meaning, however (according to your own stated views) does not have this objective quality at all. It is therefore impossible for atheists to talk about meaning at all, because meaning can never escape the subjective in atheism.