This is the way it ought to work, but often does not. Or, when your peer group associates criminal or antisocial behavior with positive attributes.
Shaming does not work in a large population of antisocial people. Religion is not THE answer however for a large population of people it is necessary (currently).
"People feel good when they help ...". No argument. But is morality just about the feels? No, it isn't.
Now, if one believes in a creator that is many orders of magnitude (or infinitely) more intelligent than a human, sure, saying that they probably have a better insight into morality and we should listen to them makes sense. But it would be because of their greater ability to understand what is moral, not them being the law maker of morality.
Well, because the god can stick you in a fire for all eternity if you follow the human's moral code instead. That's not really a great case for the soundness of their moral teachings but nonetheless presents a compelling argument for obedience.
You say that, and it's good that you did because the arguments you're making don't work together to prove your point in the way that you think they do. What about a godless universe makes morality impossible to justify? Is it that god is the only possible source of morality or meaning or value or something? Because you haven't proven that and can't just take it as axiom.