I found MisterChris's argument interesting because I have never seen it before (and it resonates with my scientific thinking). Here I will try to cross examine with Socrates method to show if it holds water or not.
A. Intuition.P1: If morality is objective, then we can expect virtually universal use of a standard set of moral principles.P2: All humans use and appeal to this standard, if only subconsciously.C1: Morality is objective.Let’s work through this. Whenever two men have a dispute, the one side tries to convince the other that they have violated a standard of good conduct that they both share, while the other argues that they have not violated such a standard.If there were not a shared standard between them, such an argument would be pointless, as one could simply say “to hell with your standard.” If that were the case, we could not condemn genocide, rape, or any other cruel act because we could not compare it to a universal standard of good conduct. Similarly, you can not argue that a football player committed a foul if the rules of football are not universally true.Since we DO make disputes/condemnations, this universal standard must exist. Thus, we affirm daily that morality is indeed objective.
Obviously, we already see problems with P2, the contradictory nature of humans. Kant claims that it is the universal law that makes an action moral. John Stuart Mill claims that the consequence with greater good is moral. In a dispute between Kant and John Mill alone, if they solidly believed in their philosophy, they could arguably both say "to hell with your standard", and stand by their personal claims. Therefore, I will produce a more easily backed premise based on MisterChris's logic.
P1: If morality is objective, then we can expect virtually universal use of a standard set of moral principles.P2: The vast majority of humans use and appeal to this standard, if only subconsciously.C1: Morality is objective.
P2 seems weaker, however, there can still be an objective standard even if only a majority accepts it. For example, it has been proven beyond a doubt that the Earth is Round. But some people lack scientific thinking, or have no experience with experimentation, and therefore believe that the earth is flat, contradicting this idea. But as the majority of scientists and educated men have managed to find and agree on this objective fact, they have successfully established its objective nature.
However, there are still problems even with this more lax expectation. There are often undecidable problems within reality. Trump vs Clinton was nearly a tie in popular vote, for example. In addition, the "majority of humans" might still believe in something wrong, such as the earth being center of the universe, before exploring outer space. Due to lack of information, they could not find the objective truth.
Therefore, I propose an overhaul to the entirety of the universe as a standard. The reasoning behind this is that the vast majority of universe has to follow certain laws: Conservation of matter, speed limit of light, equal and opposite motions, so on and so forth. We have gathered from countless evidence in order to prove the universe's age, not merely from humans or earth, but from the entirety of the universe itself. It would be cherry picking to pick from Earth, after all.
So the whole repealed argument can be like this:
P1) What is objective (ex. science, math, truisms) can find overwhelming evidence in fact within the whole universe
P2) The whole universe follows certain laws and rules, patterns, among these which are our actions
C) Therefore, because our actions can be found to follow a certain pattern during certain times, this can be overwhelming evidence combined to show objective morality.
(however, the problem is that science is "what should happen", not "what should I do", which is a whole other can of worms...)