I think I may be able to cut right to the chase by reviewing where we are at at this moment in your argument. Maybe not but it is worth a try.
You are not arguing that there is a god so I can safely dismiss the idea as the default on any undemonstrated claim can be dismissed and you are disinclined to prove it. Remember that is part of my most basic axiom.
You are arguing that if there is no god there can be no objective morality and I have already dismissed god so I can also dismiss objective morality.
The alternative to objective morality is to you definitionally nihilism. If nihilism is logically necessary (and your argument so far supports that) then you and I are both nihilists. Which does not stop you from trying your best to be your own personal idea of what a good person is like, which is clearly not a moral opinion so I'm not sure what to call it. You clearly fall short of that idea and you don't think the idea you have is perfect but you are trying. These are also not moral opinions and I'm not sure what it makes them.
It also does not stop me from trying my best to be my own personal idea of what a good person is like, which I maintain is a moral opinion unless you can otherwise explain the phenomenon. I clearly fall short of that idea and I don't think the idea I have is perfect but I am are trying. These are also, I maintain, moral opinions unless you can explain what it is they in fact are.
I am not advocating for anything I can not prove exists I am just being told that I am using the wrong words. I kindly ask you to take the concept I have in this conversation as moral intuition (ones personal idea of what a good person is like) and supply the term that best describes it.