Most (universal) ethical systems which I have encountered come up with some kind of a priori rule (e.g. "maximize happiness and minimize pain", or the categorical imperative) and then apply that rule to various situations in order to figure out what course of action is ethical.
I'm going to label two parts of your question that come from the same paragraph.
 But I think that an ethical statement such as "murder is wrong" is actually a psychological statement about how (the vast majority of) humans conceptualize murder. In other words, "murder is wrong" means "If you ask people whether murder is wrong, the vast majority will say yes." If we have a moral statement which has no large majority on either side, we may deny both the statement and its opposite as in error theory ("[Political issue X] is not a moral issue at all.").
 Alternatively, we may claim that there is a truth to the matter but that cultural and social differences are obscuring it from measurement ("Either [X] is moral, or it's immoral, but it's so politicized that we can't get a good empirical measurement right now. Maybe in a century or two things will settle down.").
Note that  and  contradict one another, but you don't seem to have noticed. According to , the view you want to take in  is false because there is nothing to discover.
You should concentrate on actually being able to state a particular position without contradicting yourself. You might say you are just listing two different ideas, but if you are doing that it's impossible for me or anyone else to tell which position you are advocating.
This has the advantage that it tends not to disagree with people's intuitive ideas about ethics,
No. Your view, whatever it is, agrees with your intuitive ideas about ethics, which I'd guess are a muddle of ideas you've picked up more or less by accident because they happened to be around when you were doing a philosophy course or something.
while still being (arguably) a form of moral realism. It has the disadvantage that ethical positions may shift over time as attitudes change.
Position  has many disadvantages.
First, how many people constitute the vast majority of humans and why? Your position can't answer that question because there is no non-arbitrary answer.
Second, on any issue on which there is a disagreement you should express no position. And the more people adopt your idea, the fewer people will express a position on controversial topics, so those issues will never be settled if your position becomes widespread. Also, since your moral position is that morality is about what the vast majority of people think is moral and the vast majority of people would not accept your position, your position implies its own falsehood.
Third, your position is completely unable to explain why people change moral positions over time. the root of the problem is that  doesn't recognise any objective morality that people could discover apart from what views people actually hold. So  is just subjectivism dressed up by saying a majority have to agree on something: the whims of a majority define morality.
Fourth if you're going to deny a load of issues about what to do are moral issues, you would leave people with no way of deciding what to do on those issues.
Fifth, I think you might be a bit surprised about how much stuff is not decided on your view. For example, there are whole countries where the prevailing view seems to be that it's okay to torture and murder homosexuals. So you should express no opinion on that since we don't have an agreement of the vast majority of people. The same is true of whether abortion should be legal.
Finally, in many cases where the majority might have an opinion, your position is impractical as a guide to action. 'Should I have an abortion?' 'I don't know. I would have to hold a poll to determine the majority opinion on what you should do in your particular circumstances.'
Position  is simply nonsense. If morality is objective, then it's not a matter of measuring what people think. If  is true, then there is no question of saying that there might be an objective fact of the matter about morality because you have defined morality as what the majority of people want.
I recommend that you read some Ayn Rand since she is good at making short work of positions like the one you expressed above. See the title essay in "Philosophy: who needs it" and "The virtue of selfishness".