Romans 3:21
But now the righteousness of God without the the law is manifest, being witness by the law and the prophets;
The righteousness of God is neither an attribute of God nor the changed character of the believer.
There you go forming doctrine from verses taken in isolation without considering all the other applicable verses.
How do you fit the following into your doctrine that righteousness is communicated to us from Christ?
Act 10:35 But in every nation he that feareth him, and worketh righteousness, is accepted with him.
Seems we have to work righteousness, it is not merely an external characteristic of another applied to us, it is the result of being converted and responding to the righteousness infused in us from Christ.
Rom 6:16 Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness?
Here we see that obedience is what brings us unto righteousness.
Eph 5:9 (For the fruit of the Spirit is in all goodness and righteousness and truth;)
This verse tells us that righteousness is a fruit, something we produce through our faith. Not some outside characteristic applied to us.
2Ti 3:16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
If righteousness was Christ and His righteousness was applied from outside independent of our actions then scripture would have no purpose in teaching us how to be righteous.
1Jo 3:7 Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteous.
Here we see that we can be righteous as He is if we do righteousness. This certainly isn't a righteousness applied externally.
Jam 2:22 Seest thou how faith wrought with his works, and by works was faith made perfect?
Jam 2:23 And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God.
Jam 2:24 Ye see then how that by works a man is justified, and not by faith only.
And of course we have James who once again has to teach that righteousness comes through faith, but it is a faith that is perfected and kept alive by works.
2Pe 2:20 For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning.
2Pe 2:21 For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them.
2Pe 2:22 But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
This too is a problem for your doctrine as we see that even after we learn of Christ and know the way of righteousness that we can turn from the holy commandment and leave this righteous way. If righteousness was something merely imputed to us there would be no way to turn from the holy way of righteousness and we would be saved once forever, but we see that Peter shows this is not the case. Some return to thier wallowing.
You really should do a complete word search before you start trying to formulate doctrine in a vacuum.
As defined in Romans 1:17, the righteousness of God is Christ himself, who met every demand of the law for us in our stead, and is "made unto us......righteousness"
That is one use of the word but it is not the only meaning applied to it by scripture and to focus on it in isolation is bound to bring errors, as you have shown it to.
I Cor 1:30. God's righteousness is is demonstrated and communicated to us through the cross.
But not merely imputed - it must infuse us change us convert us so we can do the works that perfect our faith.
Just as Jesus and sin have nothing in common, so too the righteousness was not manifest in keeping the law but was manifest at the cross when "He (God the Father) hath made Him (God the Son) to be sin for us, who knew no sin; that we might be made the righteousness of God in Him (II Cor 5:21).
It was not manifest in the law because the Israelites tried to fulfill the letter of the law to merit their salvation. We know that we are to fulfull the spirit of the law through love and that makes it possible for us to keep the righteousness of the law by cooperating with His free grace.
Rom 2:26 Therefore if the uncircumcision keep the righteousness of the law, shall not his uncircumcision be counted for circumcision?
Rom 8:4 That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
In these two verses we see Paul teaching that righteousness can come from the law and we can now keep the righteousness of the law (once we understand we are called to fulfill the spirit of the law through love).
We are justified when the righteousness of God is applied to us "though faith in Jesus Christ".
Yes but it is not merely imputed it is infused in us so we become converted.
This righteousness is placed upon us as a cloak when by faith we receive Jesus as Saviour.
Do you have a scripture verse to support this cloak idea? If we are merely covered by His blood and we are still sinful underneath it is playing the Father as a fool. No His blood must wash away our sins, change us fundamentally and we must remain changed, with a living faith perfected by works.