At its core,

[MadMojoMonkey]

I agree that there are grey areas, but I'd argue that in majority of cases there are quite clear objective verifiable rights and wrongs.

Are they so clear that you'd expect widespread consensus agreement from all people?
Or is tyranny of the majority enough?
Is tyranny of the majority moral?
If so, by what argument? (Recall: majorities have decided that slavery is moral, genocide is moral, etc.)

I.e. that guy thinks murdering humans is a fundamental human right, and necessary to the growth of human cultures. Is it morally OK to disregard his position on this? Is it morally OK for a majority to assert moral dominance on others simply because they outnumber them?

Ok let's try. First, a crime has taken place and we need to decide what to do with the offender. Does killing the suspect 1) produce less suffering and 2) produce more happiness than not killing him? Killing him may give some small sense of justice and resolution for the loved ones of the victim (if there is one), but produce incredible suffering for the suspect. I would say this is a great example where morals of some people are completely out of whack, and it would be somewhat trivial to demonstrate it.

In the war scenario, again, will starting a war minimize suffering (of humans, or life on the planet, not just some arbitrary bunch of people) and maximize happiness? I can't think of many scenarios where this would be the case. Another great example where a more accurate moral compass would be needed.

For the criminal, see above. Is tyranny of the majority an acceptable way to determine which moral argument is "really moral."

For the war, similar problem. The problem is that the people you're warring with have congruent arguments about why it is YOU who is the morally corrupt aggressor, while they are the righteous defenders of their cultural and traditional way of life.

You're giving me way too much credit. Just because I can't come up with one on the spot doesn't mean it can't be done.

That's fair, but not at the same time. You assert this should be possible, but you have no idea how to make it happen.
This is certainly worth exploring and noting that you are not the first to posit this idea. It's worth examining how and why other similar suggestions have failed to yet yield any fruit.

I assert that this is a common human feeling / reaction to this topic, and that when you dig past what seems moral in one culture seeming immoral in other cultures, and neither has any convincing reason for their opinions, it becomes less clear. I.e. I assert that it seems simple when you assume that what is moral in your local area is the only working moral framework.