I think your argument makes a mistake right here. It assumes that a person needs a reason to choose to be good. I believe that is false. I don't think a person needs a reason to be good any more than he needs a reason to make art—or to take a walk.

I am not a theist, nor do I object to theism. I believe there is good in all people.

The idea that a person needs a reason to be good presupposes something bad about theists—something that I think is generally untrue.

It suggests that, unless there is a God to judge you, you would choose to be bad. If that were a case, a good non-theist would be a very admirable person, and a good theist would be a practical person who fears the judgement of a deity.

I believe that, for the most part, non-theist and theists who are good behave with beneficence and empathy because that is just how they are.