I think this might be the nub of it all… “the spirit/intent” – Jesus elsewhere says this in-kind…
Mt 23:23-24 “Woe to you, scribes and Pharisees, hypocrites! For you pay tithe of mint and anise and cummin, and have neglected the weightier matters of the law: justice and mercy and faith. These you ought to have done, without leaving the others undone. Blind guides, who strain out a gnat and swallow a camel!
Um.
“Do not murder”, “Do not commit adultery”, “Do not swear falsely but fulfill your vows to YHWH”, could not be more obviously laws from God, as they’re just citations from the Ten. “Eye for an eye and a tooth for a tooth” is a key Torah quotation from God in Exodus, Lev, and Deut. “You shall love your neighbor” is not only a direct command from Lev 19:18, but Jesus later calls it one of the two Great Commandments upon which all the Law and Prophets hang.
No Jew in the audience would have thought anyone but God had said these “to those of old”.
“…and hate your enemy” is an addition by the halakah, no doubt meaning to summarize a bunch of commands (like refusing to ally with Ammon or Moab nor to let them join the assembly of YHWH – though if that was what was in mind, it’s interesting that YHWH follows up with insisting that Egypt and Edom must not be detested, particularly Edom for being brothers with them!)
“…whoever murders will be in danger of the Sanhedrin” would have been a reasonable addition under the local cultural circumstances, though the emphasis ought rightly to be any sin no matter how small being in danger of God’s judgment.
It seems obvious enough that “the old laws” of verses 33, 38, and 43, were NOT to be “abandoned entirely”: the whole point to restricting a promise to “yes yes” or “no no” was to avoid swearing falsely by YHWH thus taking His name in vain; and I can’t imagine why anyone anywhere at any time would think Jesus of all people expects us to entirely abandon loving our neighbor as ourselves, especially since He follows up that reference immediately with loving even our enemies as our neighbors! (Arguably, He doesn’t even expect us to abandon hating our enemies for some values of ‘hate’.) The usage of eye for an eye as positive justification of equal counter-attack, instead of limiting punishment, was to be abandoned, but fair punishment was not to be “entirely abandoned”; nor do the social examples given by Jesus involve abandoning fair punishment concepts, they involve rooting out the attitude that leads to appealing to “eye for an eye” as an excuse for violence. Turning the other cheek, in that cultural situation, would even have been tantamount to asking for a fair fight!
At any rate, no, none of what Jesus says there involves outright breaking Torah; so cannot count as parallel examples for the idea that Jesus would (much less ever did) actually break the Sabbath.
The apostle Paul wrote:
19 ¶ For though I am free from all, I have made myself a servant to all, that I might win more of them.
20 To the Jews I became as a Jew, in order to win Jews. To those under the law I became as one under the law (though not being myself under the law) that I might win those under the law.
21 To those outside the law I became as one outside the law (not being outside the law of God but under the law of Christ) that I might win those outside the law. (1Cor 9: 19-21 ESV)
In verse 21, Paul seems to indicate that one can be outside the Mosaic law, that is not under it, and still be under the law of Christ. Doubtless the law of Christ is expressed in Matthew 5, 6, and 7.
If one can be outside the Mosaic law and still be under the law of Christ, either:
Personally, I subscribe to the second.
Is there a third option of which I am not aware?
Ro. 1:18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness, 19 because what may be known of God is manifest in them, for God has shown it to them. 20 For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse, 21 because, although they knew God, they did not glorify Him as God, nor were thankful, but became futile in their thoughts, and their foolish hearts were darkened.
Ro.2:12 For as many as have sinned without law will also perish without law, and as many as have sinned in the law will be judged by the law 13 (for not the hearers of the law are just in the sight of God, but the doers of the law will be justified; 14 for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, 15 who show the work of the law written in their hearts, their conscience also bearing witness, and between themselves their thoughts accusing or else excusing them) 16 in the day when God will judge the secrets of men by Jesus Christ, according to my gospel.
Psalm 19:1
The heavens declare the glory of God;
And the firmament shows His handiwork.
2 Day unto day utters speech,
And night unto night reveals knowledge.
3 There is no speech nor language
Where their voice is not heard.
4 Their line has gone out through all the earth,
And their words to the end of the world.
I think there may be a third law. Abel, Enoch, Noah, Seth, Abraham, Isaac and Jacob, may have walked by it. It would be the law spoken of in the above verses. Something that was set in place before Sinai. If I am correct they walked by it as they “walked with God” in some measure of fellowship and integrity that was strictly the product of their being in fellowship with the I Am as true men, friends of God.
This might be …“the light that lighteth every man who comes into the world”, a testimony in the heart of every being that it is created, and an image of the imprint of the creator within and a reflection of that image in the things created, so that,
“since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse”…
“for when Gentiles, who do not have the law, by nature do the things in the law, these, although not having the law, are a law to themselves, who show the work of the law written in their hearts.”
having not had the law of Moses, as the forefathers did not, and as multitudes who lived in the outlying world without the lampstand of Israel, and as multitudes even until today, having never heard or seen a certifiable gospel, are perhaps accountable to this third law, and judged by it on the Day of God, “who ‘will render to each one according to his deeds’: eternal life to those who by patient continuance in doing good seek for glory, honor, and immortality; but to those who are self-seeking and do not obey the truth, but obey unrighteousness—indignation and wrath, tribulation and anguish, on every soul of man who does evil, of the Jew first and also of the Greek; but glory, honor, and peace to everyone who works what is good, to the Jew first and also to the Greek. For there is no partiality with God.”
It would be the law written on the hearts of every man since the beginning, then further illuminated by Moses, then finally fulfilled in Jesus the Messiah.This is actually the train of thought that first set me on the path of “universal reconciliation and the restoration of all things.”
From the beginning(Alpha) the invisible attributes of His eternal power and divine nature are clearly seen, in the end(Omega) all things will become partakers of the divine nature by His eternal power as the creation is set free from futility iinto the glorious liberty of the children of God and as God becomes all in all. So I might describe that third law as “the law of the eternal power and divine nature of the Creator”.
No wonder “It is finished”
The work of God ended and the Sabbath rest revealed as our beloved Savior breathed His last breath, revealing once and for all, the etrnal power and divine nature of God to all, even the principalities and powers of darkness.
Glory to God 
I subscribe to the second, too, but that doesn’t mean Jesus was breaking the Mosaic law which He specifically said He came to fulfill and not to abolish.
Considering that Jesus repeatedly indicates that His mission, though also to Gentiles, is first to the Jews, even to the point of denying that His mission is currently to the Gentiles if the two missions seem to be conflicting, your quotation from Paul as an example of following Christ’s evangelical actions actually weighs in favor of Jesus showing His faithfulness to the Father (whether in a trinitarian or any non-trinitarian way) by keeping basic Torah – and even going so far with ‘basic’ Torah as to keep the Feasts!
Even when He chooses not to go to Jerusalem for Passover in the middle year of ministry, He still effectively keeps Passover by His own power and authority (in the feeding of 5000 incident, which was yet another of those high-identity/authority claims – as was the feeding of the 4000 in pagan territory well before Passover, apparently during an early spring festival of theirs, the following year.)
For though (especially as God Most High… or even a lesser lord or god in comparison to us 
) He is free from all, He made Himself a servant to all, that He might win more of them, becoming as a Jew to the Jews, in order to win the Jews: to those under the law He became as one under the law, though not Himself under the law, that He might win those under the law.
But as it happens, Jesus did not typically become one outside the law to those outside the law; not because He couldn’t, but because He thought He should be reaching out to His Jewish people first.
I do think Jesus stepped outside the subordinate Law, the 600ish commands for keeping the 10ish commands – I could give some fairly subtle examples of that (such as going under that tree for Zacchaeus), and some fairly unsubtle examples of that (touching lepers to cure them) – but to step outside the 10(ish) commands would be on par with committing murder, or adultery, or idolatry against God.
You think that Jesus fulfilling the law was his obedience to the commandments?
My thought is that He was the fullfillment of the prophecies in “the law and the prophets”. He stated that Moses wrote about Him. Thus, for example, He fullfilled that which Moses had written about Him. He didn’t come to abolish the law and the prophets, and establish something entirely new, but was the fulfillment of them—He established by his life and works what was really intended by them.