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.