I don't see us saying something different, and I appreciate you bringing this out more.May I tweak the above just ever so slightly, even though I think you are saying the same thing... We walk by faith right? So...if we believe that old man is indeed dead, and the new resurrected man we are today is alive in Christ... The fruit of that faith, the fruit of that belief, the result of our trust in what God has declared is in fact true, is a the life lived in righteousness and holiness, as presented in Romans 8. The battle we have presently is over self. We are tempted in the flesh to believe that we are carnal and still living in the flesh (and others confirming that lie isn't helpful). But we are to believe God. The life we live is a refection of our faith. If Christians don't live lives of love, joy, peace, contentment, kindness, generosity etc, it isn't because they don't believe in the law, or because Jesus died in their place, is because they don't believe they are dead. And if we are dead in Christ, so also are we alive in Him. Which is what Paul was saying to overcome by following his example by dying daily... Affirming by faith what God has already declared to be true.
It's because this is true that we have victory over flesh when we live this way, by our faith that what God says is true.
Much love!