For one to truly understand imputed righteousness of Christ, one must first understand the source of Christ's own righteousness.
That is your error. It is easy to fall into error when you stray from the scriptures and try and read things into the text. Many of the other things you say are true but your foundation is in error.
Nowhere in the Bible does it say that the righteousness of Jesus Christ is imputed to the believer.
What it does say is that
FAITH is imputed as righteousness.
Rom 4:3 For what saith the scripture?
Abraham believed God, and it was counted unto him for righteousness.
Believed - pisteuō - G4100
pist-yoo'-o
From G4102;
to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to entrust (especially one’s spiritual well being to Christ): - believe (-r), commit (to trust), put in trust with.
Rom 4:20 He staggered not at the promise of God through unbelief;
but was strong in faith, giving glory to God;
Rom 4:21 And
being fully persuaded that, what he had promised,
he was able also to perform.
Rom 4:22 And
therefore it was imputed to him for righteousness.
Faith - pistis - G4102
From G3982;
persuasion, that is, credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher), especially reliance upon Christ for salvation; abstractly constancy in such profession; by extension the system of religious (Gospel) truth itself: - assurance, belief, believe, faith, fidelity.
Justification is by faith because it is by faith that the heart is purified.
Rom 3:28 Therefore we conclude that
a man is justified by faith without the deeds of the law.
Act 15:9 And put no difference between us and them,
purifying their hearts by faith.
When someone forsakes their wickedness in repentance and is broken on that rock of Christ they are in a position to yield to God. A wild horse must be broken before it will submit to a rider and it is no different with a sinner.
Jas 1:21 Wherefore lay apart all filthiness and superfluity of naughtiness, and receive with meekness the engrafted word, which is able to save your souls.
Once the wickedness has been forsaken the new believer then yields to the working of God in them by faith. This produces purity of heart.
Jesus said it like this...
Joh 15:3 Now
ye are clean through the word which I have spoken unto you.
Joh 15:4 Abide in me, and I in you. As
the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
Joh 15:5 I am the vine, ye are the branches:
He that abideth in me, and I in him, the same bringeth forth much fruit:
for without me ye can do nothing.
You are correct when you quote Titus 3:4-6 because it is God working in us. We yield to that work. This is why Paul would say...
Php 2:5
Let this mind be in you, which was also in Christ Jesus:
Then a few verses say...
Php 2:13 For
it is God which worketh in you both to will and to do of his good pleasure.
God is the author of our salvation but it is via an obedient faith that we cooperate with the author and thus the fruit of salvation is produced. Thus we are saved by grace through faith.
It is error to say that the righteousness of Jesus Christ is imputed to you because righteousness cannot be transferred. Righteousness is something that we do.
1Jn 3:7 Little children, let no man deceive you:
he that doeth righteousness is righteous, even as he is righteous.
What we do is we partake in the divine nature after having escaped the corruption that is in the world through lust.
2Pe 1:4 Whereby are given unto us exceeding great and precious promises: that
by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust.
Nature - phusis - G5449
From G5453;
growth (by germination or expansion), that is, (by implication) natural production (lineal descent); by extension a genus or sort;
figuratively native disposition, constitution or usage: - ([man-]) kind, nature ([-al]).
The divine nature is something that grows in us as we yield to the working of God.
Gal 4:19 My little children, of whom I travail in birth again
until Christ be formed in you,
Look at this verse...
Rom 3:22 Even
the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
It's talking about the exact same thing as I was elaborating on above. It is the divine nature, the mind of Christ, the righteousness of God. It is not transferred to us, rather, it manifests in us through us yielding to God through abiding in Jesus Christ.
It is through the knowledge of Jesus Christ that God has given us all we need to attain life and godliness.
2Pe 1:3 According as his divine power hath given unto us all things that pertain unto life and godliness, through the knowledge of him that hath called us to glory and virtue:
It is a beautiful thing.
After all this is the whole purpose of the commandment.
1Ti 1:5 Now
the end of the commandment is charity out of a pure heart, and of a good conscience, and of faith unfeigned:
It is a beautiful thing.