The major problem of your theory is that it is too restrictive in regard to the audiance being addressed. This is a GENTILE congregation and this is made very clear in Romans 15:15-23
15 Nevertheless, brethren, I have written the more boldly unto you in some sort, as putting you in mind, because of the grace that is given to me of God,
16 That I should be the minister of Jesus Christ to the Gentiles, ministering the gospel of God, that the offering up of the Gentiles might be acceptable, being sanctified by the Holy Ghost. {offering up: or, sacrificing}
17 ¶ I have therefore whereof I may glory through Jesus Christ in those things which pertain to God.
18 For I will not dare to speak of any of those things which Christ hath not wrought by me, to make the Gentiles obedient, by word and deed,
19 Through mighty signs and wonders, by the power of the Spirit of God; so that from Jerusalem, and round about unto Illyricum, I have fully preached the gospel of Christ.
20 Yea, so have I strived to preach the gospel, not where Christ was named, lest I should build upon another man’s foundation:
21 But as it is written, To whom he was not spoken of, they shall see: and they that have not heard shall understand.
22 ¶ For which cause also I have been much hindered from coming to you. {much: or, many ways, or oftentimes}
23 But now having no more place in these parts, and having a great desire these many years to come unto you;
Second, God's law is not restricted to Moses but in regard to the Gentiles it is inclusive of the law written on the conscience (Rom. 2:14-15)
14 For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves:
15 Which shew the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another
Third, we are talking about the law in regard to the "INWARD man" not the outward man in distinction to 'I" and Paul teaches that the law of God has been written upon the heart of the inward man and that the inward man has been created in "true righteousness and true holiness"
2 Cor. 3:3
Forasmuch as ye are manifestly declared to be the epistle of Christ ministered by us, written not with ink, but with the Spirit of the living God; not in tables of stone, but in fleshy tables of the heart.
Eph. 4:24
And that ye put on the new man, which after God is created in righteousness and true holiness.
Paul instructs BELIEVERS to "put on" this inward man for the very reason discussed in Romans 7:14-25 as there is no victory over indwelling sin any other way. Putting on the inward man is done by the power of the indwelling Spirit of God (Rom. 8:12-13).