@Gripphon - Here goes a tentative answer. I am going to try to do my best not to use overly esoteric philosophical terminology, but this is somewhat abstract, so I hope it makes sense. First, let me propose three strong impressions that are basic qualities of human experience.
I-1. The material world exists and operates according to universal, observable principles. (The study of this phenomena by human agents we call science.)
I-2. I have free will; I can make choices.
I-3. Some choices should be made and some shouldn't. (The study of this by human agents we call morality.)
Let's begin with the first impression: that the material world exists and behaves according to universal principles. This is a reasonable impression of human experience. As Kant observed, this is ultimately subjective and unverifiable. More recently, philosopher Hilary Putnam (who is actually still living) has restated this problem with much clarity. Furthermore, in some cultures there are many who deny the existence of the material world, and even certain religions that are entirely predicated on such a denial. But despite that initial problem, I accept the first impression as truth without much problem. If we go further and maintain that the material world is all that exists, however, this denies the second two concepts. If man and other creatures are no more than the sum of chemical reactions in a group of molecules, then despite the great complexity in these reactions, there is no possibility for variation. These reactions would have always occurred in the way they did, because the material world is government by universal principles that do not vary. In a materialist conception that denies the metaphysical/supernatural, the world that exists is the only one that could exist, as it is inexorably subject to the principles that govern it. This means the conception that the material world is all there is, is ultimately a deterministic one that does not allow for free will.
As morality is the result of free will, if we believe the material world is all that there is to reality, then we ultimately deny free will and morality, so talking about them doesn't make sense. They are illusory, and so is our talking about them. Now, is this a complete explanation for human experience? It is logical, but it denies two of the most basic impressions I named earlier. We should note that the second proposition, I-2, that we have free will, is what we have largely understood is the precondition to understanding I-1--that is, scientific inquiry is the result of free human choice. Now, you're probably thinking, well sure I agree with I-1 and 2, but what about the third impression? Is it really a self-evident facet of human existence like the other two? Well, I-3, the proposition that some choices should be chosen over others, is what has driven scientific inquiry. The high level of contingency in these propositions strongly suggests a causal relationship that in turn points to the truth of all three. It could be that this relationship is pure coincidence, and thus a large part of human experience is in truth an illusion, but I don't think so. It seems quite verifiable that I have free will. Although I could explain away my own free will as some sort of illusory mental interpretation of a deterministic world, I can test my free will and that of others according to a fairly scientific process and verify it without much problem. Someone can ask me to choose to throw a ball a hundred times, and each time I can easily respond by throwing the ball. It does not matter that the chemical and material processes in my body are functioning quite differently at each time I am asked, I am still able to make the choice. This process can be replicated ad infinitum with any human agent capable of throwing a ball. Thus, while morality can't be subjectively demonstrated, it seems that free choice quite easily can, and is even observable in the material world. This is really quite astounding: the existence of the metaphysical world can be proven by experimentation in the material world.
Now if we affirm both I-1 and I-2 as true, we've affirmed quite a lot, because in affirming free will, we've affirmed that something exists beyond the strictly material realm--this would be described as metaphysical or supernatural: two terms that merely mean "beyond" the natural/material. Now again, this is a fairly monumental truth, as it not only demonstrates that a supernatural/metaphysical component of reality exists, but also demonstrates that this metaphysical component can profoundly impact the material world. Civilizations are built, the secrets of nuclear power are unlocked, men are put on the moon--all as a result of a metaphysical process of free will. In light of the magnitude of the ramifications of choices that take place in the metaphysical realm, morality would seem of the utmost importance. And this is generally how it has been understood throughout human history.
Now, as to your question of how and why moral truth appears subjective, and possible solutions, we should examine the origin of its problematic nature. Scientific experiments can be conducted because the truth we seek is truth regarding the material world. These truths are constants--they are "what is." We may discover them precisely because they cannot be violated, and as such are always observable. Morality, on the other hand, is not the study of laws that cannot be violated. It is rather the study of truths that may be violated or affirmed--they are "what should be." This is where the problem arises. There are two problems. The first is that because these principles can be violated, they cannot be verified through experimentation as they are not constants. The second is that morality, as the study of the proper function of the human free will, ultimately isn't the study of a material truth, but of an immaterial/metaphysical/supernatural truth. This is why I ultimately seek answers to questions of moral truth through active inquiry into the supernatural/spiritual/metaphysical realm. To answer your final question, I don't ultimately believe we can divine moral truth so clearly through the same processes of observation that work so well with the physical world. So, I agree that the basic quandary you have posited indeed exists.
Now, this does not mean that we can't make some fairly concrete ethical observations. It's just that it takes a lot more effort than it does to verify truths in the material realm. Many philosophers have been able to speak fairly clearly about these things, but it just takes tons of space--something this post is already proving! A few that come to mind are Aquinas, Kant, and Leibniz. In the 18th century Jeremy Bentham even developed an entire system of felicific calculus for making moral decisions. I will hopefully post a bit more about it tomorrow, but I hope that explanation helps make a little sense of where I'm coming from as far as seeking answers for moral questions outside the material world. I realize I haven't as much addressed the problem of disentangling morality from culture, but I'll try to explain that a bit more tomorrow.
To be sure, it'd be far easier just to say morality was subjective and leave it at that. I think that's actually a more defensible position intellectually, just because it is quite reductive, but I also think it's quite important to make moral judgments that transcend culture. Like I said earlier in the thread, if morality is merely a product of culture, we have no more right to decry genocide in Darfur than we have a right to judge the taste of their cuisine.