Well if sin isn't really transfer over, then neither is righteousness really tranfered over to the soul, when one believes, since it is the same term beeing used. Which means the soul is not really righteous, and it can't be justified, because does not justify the "not really righteous" because they are seen as ungodly still. That is why faith without works is dead.
It's obvious you don't understand the biblical concept of imputation or how God was in Christ justifying and reconciling us to Himself.
When Jesus hung on the cross, our sins were imputed to Him. And His death thereby acquitted us of quilt and condemnation and justified us (the soul) accordingly. It also reconciled us to Him.
It didn't "make" us righteous by changing the substance or nature of the soul (our flesh or spirit), but rather reckoned and accounted us (the soul) as "righteous" and without sin, in Him. And in so doing, God forgave, justified and reconciled us to Himself.
Does that make us (the soul) sinless at the present time? Of course not. We still sin as before, and we do so according to the flesh. Read the following:
1Jn 1:8
If we say that we have no sin, we deceive ourselves, and the truth is not in us.
1Jn 1:9
If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
1Jn 1:10
If we say that we have not sinned, we make him a liar, and his word is not in us.
And, Paul tells us exactly what it is that sins. It's the sin nature of the flesh. The flesh that dwells within us:
Rom 7:17 Now then it is no more I that do it, but
sin that dwelleth in me.
Rom 7:18 For I know that in me (that is,
in my flesh,)
dwelleth no good thing: for to will is present with me; but how to perform that which is good I find not.
Rom 7:19 For the good that I would I do not: but the evil which I would not, that I do.
Rom 7:20 Now if I do that I would not,
it is no more I that do it, but sin that dwelleth in me.
The flesh has been crucified with Christ, however it's not yet been rendered inactive. Will it be? Yes, at death when the flesh returns to dust and our spirit to God (Ecc 12:7).
Regarding righteousness. Those of faith, those who believe on
Him who justifies the ungodly, have Christ's righteousness, that is: The righteousness of God revealed from faith to faith (Rom 1:17), and imputed to our account (Rom 4:5). And that righteousness is not of our own, but of Christ:
Php 3:9
not having my righteousness, which is of law,
but that which is through faith of Christ—the righteousness that is of God by the faith,
You've yet to comment on Rom 5:6, 8, 9 and 10. Do you plan to?