But it somehow seems to me that there is no way to make morality perfecty rational. It will always require a viewpoint and choosing the viewpoint is a moral choice in itself. Is it good, per se, to decide what is good?
It's actually not difficult once you understand what ethics actually are. (I'm going to use ethics from now on because morality is a subset of ethics)
People use ethical arguments to influence the behavior of other people, either that the other person should or shout not take an action. Ethical arguments differ from other means of persuasion in that they appeal to some universal standard instead of the personal preference of the speaker. If you can convince other people that it is consistent with a universal standard of "good" to give you their best lamb every Sunday, they will be more likely to do so that if you just tell them that you want them to give you their stuff for free. We appear to have an instinctive understanding that the personal preferences of other people do not create obligations in us, but universal principles apply to everybody.
Once you know what an ethical argument is, you can examine it rationally. If somebody proposes an ethical rule that can not reflect a universal principle without creating a contradiction then the rule is false. Weeding out all the false arguments will leave behind the truth by elimination, just like how the scientific method is used to weed out incorrect hypotheses.
I think your notion of ethics is pretty ancient from our modern point of view.
We have many neural systems dedicated to these instincts and some of them are pretty specific and some even have pretty specific roles in our evolution. They seem universal because they became built into our genes due to the path we have taken throughout evolution. There are no universal principles, or at the very least, the actual important principles are badly expressed in the notion of ethics that are presented by our genes. That is exactly why we keep struggling with it. They are vague notions compared to the actual situations that occur. So our genes can only take us so far with any general notions and our reality requires a further refinement of these notions to resolve social dynamics. So we evolved things like self reflection and empathy. These are all systems that promote a certain stability in society. You have a better understanding of the fact that others are like you.
So we have these vague notions of what feels ethically right. But those notions are pretty slippery. They all relate to defining the optimum between selfishness and cooperation. So what is considered unethical in one situation can be fully acceptable in another and noone will mention anything about it out of self preservation. And of course that's what happens in reality.
The parts of your brain that arrange for your personal safety and survival will take precedence over the part that arranges for you to help out your neighbour when push come to shove.