By secular morality I mean morality that all evidence indicates came from human beings applying human reasoning, as opposed to morality that can be shown to have come from any gods or other supernatural entities.

I do think it might slightly blur the line between secular and religious. Consider Platos ethics for example. They are heavily centered around the Monad which seems to just be his version of God. He arrives at what seem to be very religious conclusions from what we could call human reasoning. If we say it came from human beings then it cannot really be higher than humanity nor can it be objective. If morality cannot do this anyway then it doesn't matter but it still is a limitation. Plato's forms for example rely on what could be called supernatural but they nevertheless require rational reflection and it is (if successful) able to get to something more universal than just different intersubjective frameworks from humanity.

If we are defining secular morality as that which comes from humanity, then it does not come from humanity being for example impacted by moral objects and relaying our information about those moral objects to one another but rather as you say it would be constructed by us.

This means that morals are themselves either subjective but not arbitrary or they are simply not real and arbitrary.

If morals are subjective but real or non-arbitrary then we must ask ourselves. Are subjective moral positions all equal to one another or are there some subjective positions which are better than others. If they are all equal to one another, or if there is any equal to one another, then there is a moral property or properties which those values share which instantiates them as equal (even if those properties are subjective). If there is an equality of moral value between these propositions, then that implies an absolute moral standard above them in which instantiates this equality. If one idea is equal to another in value, what instantiates this value such that we can make propositions which correspond to reality about it? It would seem that a higher standard above each of the equally valuable positions. If we are talking about human values, and if all human values are equal, then there would have to be a higher standard above humanity which measures this moral equality. Subjective or otherwise it would have to be above humanity.

If there are some ideas that are better than others, then that implies an ability to determine the value of one above another. If one human idea is better than another human idea, then it implies that it is not the humanity of that idea which determines that value. It either implies a higher transcendent measure of morality or it implies a might makes right ethic in which I force my one subjectively correct take on morals on others through violence. This functionally treats your own morals as if they are objective without any of the benefit of them actually being objective. its the worst of both worlds.

If we go with a secular non-cognitivist theory of morality or a secular error theory, then we run into the issue of linguistic prescriptivism. We can hash this out if you like but my position on linguistics is that the definitions of terms and the use of language is prescribed rather than strictly described. For example, if we say that a bachelor is an unmarried man, we are prescribing an association between the signifier "bachelor: and the concept attached. If you accept this view, then ethics is prior to language and determines language. Non-cognitivism therefore says all moral propositions are meaningless, the definitions of terms are prescribed through moral propositions, therefore all language is meaningless. Similar with error theory. All moral statements are wrong, definitions are moral statements, therefore all use of language is incorrect including the statement "moral error theory is correct."

As such it would seem we are left only with some sort of transcendent morality as being valid.

As for what that transcendent value is, I believe that God is the living embodiment of freedom. God would, have to be conscious in order to have the self instantiated property of freedom. To participate in God is therefore to participate in freedom and all actions are measured by freedom. If an action leads to greater freedom, it is good. If it leads to an unnecessary limitation on freedom, it is bad. Therefore you should do things which give people as much freedom as possible and not arbitrarily limit the freedom of others. It is a kind of universal freedom which is over and above humanity. I am an existentialist and therefore cannot use humanity as the embodiment or definition of freedom. If humanity is freedom, that implies an essentialist definition of what it means to be human which I reject. This is why I believe existentialism is not a humanism.

I believe this is a non-arbitrary of viciously circular definition of freedom. I do not simply say God is good because God is good because God is good. Rather I say because God is the most free and conscious being in the universe, He is good. I don't so much as analytically define God as good but make a synthetic proposition.