The "doing" of conduct begins in the heart, not with the action. "Doing" comes from "being". We bring forth who and what we are by conduct, but that conduct is according to whatever quality is in us.
If there is no imputed conduct with the imputed character, then we have no means of ever "doing" anything righteous. And righteousness IS conduct according to God's standard.
Imputed righteousness of character without imputed righteousness of conduct would mean all our conduct still comes from the old man and would be sin. Every last action and all of them combined.
God didn't leave us with no means of bringing forth our imputed righteousness. He imputed our inner conduct with our character, and it's all His. We couldn't work for it, and we can't work FROM it, either. That would be infusing our own righteousness into God's.
Righteousness means to recognize God's claim upon our lives for every standard. Of character and conduct. For "being" and "doing".
I think what's confusing to me is that I look at 'conduct' as being action, what we do. So I'm not sure what imputed conduct would be or mean. I could understand having imputed character from which our conduct comes. Doing (conduct) from the being (imputed character). But imputed conduct and imputed character is hard to follow.