We are able to keep OT law in perspective because we have things like the parable of the good Samaritan to tell us that doing good to others (including strangers) is far more important than sacrifices or things which make us unclean.
I know that nobody boasting that they keep the OT law, and deriving righteousness thereby, keeps any more than a handful of OT laws.
So I reiterate that our righteousness is imputed, and with this imputed righteousness comes works proceeding from us, which too are imputed and enabled by God. God gives us the desire to do good right from the start.
I'd have to conclude once more that that is you reading your own ideas into that.
Romans 6, or say, Galatians 5, make it very clear that the desire to work righteousness after salvation is not the case.
Else, why entire chapters like those and others completely devoted to the issue of the need to focus on working out (manifesting) the righteousness planted in one at...salvation.
Obviously, you are not noting the things that differ in Scripture between how the Law motivated righteous works, and how Grace does.
And in either case, one issue is the same in both - one's personal role in being willing to step up to the plate each time.
Case in point, of many, under the Law...
Romans 7:7 What shall we say then? Is the law sin? God forbid. Nay, I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet. 7:8 But sin, taking occasion by the commandment, wrought in me all manner of concupiscence. For without the law sin was dead. 7:9 For I was alive without the law once: but when the commandment came, sin revived, and I died. 7:10 And the commandment, which was ordained to life, I found to be unto death. 7:11 For sin, taking occasion by the commandment, deceived me, and by it slew me.
Case in point, of many that also could be cited, this side of Grace...
Romans 6:1 What shall we say then? Shall we continue in sin, that grace may abound? 6:2 God forbid. How shall we, that are dead to sin, live any longer therein? 6:3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
6:10 For in that he died, he died unto sin once: but in that he liveth, he liveth unto God. 6:11 Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. 6:12 Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. 6:13 Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. 6:14 For sin shall not have dominion over you: for ye are not under the law, but under grace. 6:15 What then? shall we sin, because we are not under the law, but under grace? God forbid. 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? 6:17 But God be thanked, that ye were the servants of sin, but ye have obeyed from the heart that form of doctrine which was delivered you. 6:18 Being then made free from sin, ye became the servants of righteousness. 6:19 I speak after the manner of men because of the infirmity of your flesh: for as ye have yielded your members servants to uncleanness and to iniquity unto iniquity; even so now yield your members servants to righteousness unto holiness. 6:20 For when ye were the servants of sin, ye were free from righteousness. 6:21 What fruit had ye then in those things whereof ye are now ashamed? for the end of those things is death. 6:22 But now being made free from sin, and become servants to God, ye have your fruit unto holiness, and the end everlasting life. 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
Verse 23 there is basically repeating what he has just said in the verses immediately previous to it - that because the Believer now has the gift of eternal life residing in him, and can now tap into it for his enablement, he should do so.
Clearly, the motivation is not...automatic.
Galatians 5:13 For, brethren, ye have been called unto liberty; only use not liberty for an occasion to the flesh, but by love serve one another. 5:14 For all the law is fulfilled in one word, even in this; Thou shalt love thy neighbour as thyself. 5:15 But if ye bite and devour one another, take heed that ye be not consumed one of another. 5:16 This I say then, Walk in the Spirit, and ye shall not fulfil the lust of the flesh. 5:17 For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would. 5:18 But if ye be led of the Spirit, ye are not under the law.
Nope - doesn't read to me like the mark of a saved person is that he is automatically behaving like one.
Rom. 5:6-8.