I am not sure that anything 'explains' the correspondence between the physical dynamics and the sensed meaning. There just is a brute fact that certain events in neurons 'look like' a kitchen table and a smartphone for me. I think Descartes says we just have to accept that there is this correspondence. The rest of our science boils down to brute facts - like the existence of charge with two options and quark colour with three and the speed of light. I am not sure of the problem here.
This takes a lot of unpacking and maybe more than we can do on a forum. Are you familiar with Frege (Sense and Reference) and, more importantly, Grice? Frege didn't really get sense right in that he talked in terms of mode of presentation and there is a further sort of meaning which is just what it is like - which includes values like good and bad and phenomenal aspects like colours and smells. Grice emphasises the difference between meaning by and meaning to. He is largely interested in meaning by but works through just how much language is dependent on both coinciding in some useful way.
So I don't think there is any one 'real meaning' inputs to cells and outputs are going to have different sorts of meanings - scenarios and propositions in simple terms. Meaning shifts at every step as it goes through sequential inferences.
After thinking about it, I actually agree there is no explanation in this case. However, I would argue that this situation is fundamentally different from every other sense of the word ‘meaning’. I haven’t read Frege or Grice, and if you think they are important I would be happy to read them. The ‘meaning by’ and ‘meaning too’ seems to be an accurate distinction in terms of how ‘meaning’ is used so I will use that language. I apologize for what is a long post. But I wanted to take these ideas and refer them in terms of meaning in the sense of meaning corresponding to the physical system. This is fascinating and has some very significant consequences for philosophy.
I would define ‘meaning by’ as the way we use language to express how something means in terms of other meanings. In this case, every ‘meaning by’ is a tautology in the sense that if you started reading the dictionary you would ultimately always end up in some repeating cycle. Not to get into too much of a sidetrack but ‘meaning by’ is how I think science, logic and math works; explaining complex things in terms of more basic meanings.
In this sense, what is meant by the phrase " the speed of light in a vacuum is constant” relies on all sorts of explanations. It must be explained in terms of what light is, what a vacuum is, what speed is, what something being constant is. And we could keep breaking those down those terms into their constituent parts. However, at no point is there any layer at which there exists some brute fact. We would just keep going around in circles. I think this is because whatever the speed of light actually is, what its ‘true’ nature is, is completely unknowable. Any understanding of the speed of light must occur in some place that produces meaning and not in the nature of the speed of light itself. What something actually is is completely separate from what something means, and we can only know the latter of these things.
However, I think the meaning that comes from the correspondence between meaning and physical systems is far more fundamental. It is the meaning of what meaning is itself. It is every meaning that could possibly ever exist (in humans at least). All meanings, every meaning, boils down to the one (or possibly more) physical processes. We are defining a thing in terms of itself so it is the tautology by which all meaning is produced. What we actually mean by "The speed of light in a vacuum is constant" are the meanings that the neurons derive for each of these terms. There are other terms that mean similar to the above statement which we can use to explain 'meaning by' in terms of these other similar neural meanings. But since each of these neurons is not exactly the same as the corresponding neuron in another individual, meaning is also not exactly the same for different people.
The reason why we explain the meaning of things in terms of other things is probably evolutionary based on the fact we are social creatures. This process would try to get someone else’s “neural meanings” to fire if we can’t make that happen on the first try. In this way we can transfer meaning to someone by providing it to them in a form they can consume. At some level people all probably have similar “meaning too” and so using “meaning by” we can try and strip back layers until we get to some fundamental understanding. I think this would typically but doesn’t have to reside from the knowledge gained through the sense data and experience of the world.
The meaning of colours and smells is meaning in the ‘meaning too’ sense. As you said it is just what it is like to experience something. This is quite literally the meaning that the neuron provides when it gets the direct inputs of red without all the extra steps of ‘meaning by’. While it seems silly to ask what is ‘meant by’ red because the experience of red seems so obvious to us, what we really mean by red is the neural meaning of red. There must be something about how these neurons are set up that 'meaning too' seems obvious and the 'meaning by' is not.
Why we developed the idea of ‘meaning too’ might be due to the fact that everyone has experienced the red neuron firing. There are no reasons to have other neurons that mean similar things to red. What is no evolutionary advantage of explaining the meaning of red to someone else if they already know what red means. In contrast, describing some dangerous creature you saw to someone who has never seen it is very important. The person who hasn't seen the animal has no idea what neuron you are referring to. But if they can explain it in terms of ‘meaning toos’ or the ‘meaning bys’ they have experienced, then they can narrow down the possibilities for which neuron the person is referring to. By narrowing it down, someone else can have a very good idea of what neuron provided meaning to the first person without ever having had that neuron fire from the sense inputs.
I think the key question is in what ways ‘meaning by’ and ‘meaning too’ differ in terms of how the meaning is derived by the neuron. Perhaps they are the same thing and only differ in how many equivalent or similar neuronal meanings there are. Or perhaps it just refers to the number of steps there are between the sense inputs and the neural meaning, as at each step the input data is given some meaning. Or maybe there is some slight functional difference in how cells derive meaning. Or maybe a combination of all of the above.
I also have plenty of ideas about meaning in the context of values, morals and concepts of good and bad. I am an emotivist so I think your model fits very well but this post is already far too long.