I agree with your two statements that say:
#1. We are only obligated to keep the righteousness of/moral Law.
#2. Laws that pertained to Israel as a physical country(including health laws) and laws that pertained to the levite priesthood were suspended.
But I disagree that Jesus was not changing the Law, my brother.
I believe Jesus was making changes to the Old Law in preparation to the change of the New Covenant that went officially into effect with His death:
Biblical proof?
Jesus clearly was making changes to the Law (even before the cross):
(Which means He was not teaching primarily Old Covenant, but New Covenant):
The Old Way says:
"Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth"
(Matthew 5:38 cf. Exodus 21:23-25).
The New Way (by Jesus) says:
"But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also." (Matthew 5:39).
The Old Way says:
"Ye have heard that it was said by them of old time, Thou shalt not kill; and whosoever shall kill shall be in danger of the judgment" (Matthew 5:21 cf. Numbers 35:30-32).
The New Way (by Jesus) says:
"But I say unto you, That whosoever is angry with his brother without a cause shall be in danger of the judgment: and whosoever shall say to his brother, Raca, shall be in danger of the council: but whosoever shall say, Thou fool, shall be in danger of hell fire." (Matthew 5:22).
The Old Way says:
"Again, ye have heard that it hath been said by them of old time, Thou shalt not forswear thyself, but shalt perform unto the Lord thine oaths:" (Matthew 5:34 cf. Numbers 30:1-2, Deuteronomy 23:21).
The New Way (by Jesus) says:
34 "But I say unto you, Swear not at all; neither by heaven; for it is God's throne:
35 Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King.
36 Neither shalt thou swear by thy head, because thou canst not make one hair white or black.
37 But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil." (Matthew 5:34-37).
The Old Way says:
"And of thy mercy cut off mine enemies, and destroy all them that afflict my soul: for I am thy servant." (Psalms 143:12).
"And the city shall be accursed, even it, and all that are therein, to the LORD: only Rahab the harlot shall live, she and all that are with her in the house, because she hid the messengers that we sent." (Joshua 6:17).
"And they utterly destroyed all that was in the city, both man and woman, young and old, and ox, and sheep, and ass, with the edge of the sword." (Joshua 6:21).
16 "But of the cities of these people, which the LORD thy God doth give thee for an inheritance, thou shalt save alive nothing that breatheth:
17 But thou shalt utterly destroy them; namely, the Hittites, and the Amorites, the Canaanites, and the Perizzites, the Hivites, and the Jebusites; as the LORD thy God hath commanded thee" (Deuteronomy 20:16-17).
"They did not destroy the nations, concerning whom the LORD commanded them" (Psalms 106:34).
The New Way (by Jesus) says:
"But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;" (Matthew 5:44).
Note: Yes, I am aware that the Old Way (Old Testament) also teaches to love one's enemies (Exodus 23:4-5) (Proverbs 25:21), but this was in context to their own Israelite people, and not pagan nations. Pagan nations were to be destroyed when God commanded the Israelites to destroy them. But Jesus taught a radically different way. Love your enemies, and do good to them that hate you, and to pray for those who persecute you.
The Old Way says:
20 "But if this thing be true, and the tokens of virginity be not found for the damsel:
21 Then they shall bring out the damsel to the door of her father's house, and the men of her city shall stone her with stones that she die: because she hath wrought folly in Israel, to play the harlot in her father's house: so shalt thou put evil away from among you.
22 If a man be found lying with a woman married to an husband, then they shall both of them die, both the man that lay with the woman, and the woman: so shalt thou put away evil from Israel." (Deuteronomy 22:20-22).
4 "They say unto him, Master, this woman was taken in adultery, in the very act.
5 Now Moses in the law commanded us, that such should be stoned: but what sayest thou?" (John 8:4-5).
The New Way (by Jesus) says:
"He that is without sin among you, let him first cast a stone at her. " (John 8:7).
Even after the cross, there were changes being made:
The Old Covenant says this about circumcision:
"And the uncircumcised man child whose flesh of his foreskin is not circumcised, that soul shall be cut off from his people; he hath broken my covenant." (Genesis 17:14).
Yet, the New Covenant says this about circumcision:
"Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing." (Galatians 5:2).
The Old Covenant says this about the Sabbath:
32 "And while the children of Israel were in the wilderness, they found a man that gathered sticks upon the sabbath day.
33 And they that found him gathering sticks brought him unto Moses and Aaron, and unto all the congregation.
34 And they put him in ward, because it was not declared what should be done to him.
35 And the Lord said unto Moses, The man shall be surely put to death: all the congregation shall stone him with stones without the camp.
36 And all the congregation brought him without the camp, and stoned him with stones, and he died; as the Lord commanded Moses." (Numbers 15:32-36).
Yet, the New Covenant says this about the Sabbath:
"Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:" (Colossians 2:16).
So it appears things have changed.
This makes sense because again, Hebrews 7:12 says the Law has changed.
"For the priesthood being changed, there is made of necessity a change also of the law."
(Hebrews 7:12).
“For the law was given by Moses, but grace and truth came by Jesus Christ.”
(John 1:17).
Jesus said,
"Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil." (Matthew 5:17).
Jesus came not to abolish the Law (in the sense of destroying all forms of Law), but Jesus came to fulfill the Law (i.e. to nail to the cross those ordinances that were against us [like the Old Covenant ceremonial laws], and Jesus came to give us a more fulfilled and perfect way of obeying God via the commands that come directly from Him and His followers). For Jesus offered a more perfect way of loving God, and loving our neighbor (Which of course is only possible via if we are first saved by God's grace through faith).