EDIT: Jackson this reply hopefully answers your questions too. I didn't see it until I finished posting.
Disagree with this premise
The Levite priesthood was set up at Sinai.
.the Melchizedek was part of the Abrahamic covenant.
The statements before this one I agree with....
Disagree with timing and all these premises/ conclusions
Exodus 19:5-6
5 Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine:
6 And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel.
7 And Moses came and called for the elders of the people, and laid before their faces all these words which the Lord commanded him.
8 And all the people answered together, and said, All that the Lord hath spoken we will do. And Moses returned the words of the people unto the Lord.
9 And the Lord said unto Moses, Lo, I come unto thee in a thick cloud, that the people may hear when I speak with thee, and believe thee for ever. And Moses told the words of the people unto the Lord.
10 And the Lord said unto Moses, Go unto the people, and sanctify them to day and to morrow, and let them wash their clothes,
11 And be ready against the third day: for the third day the Lord will come down in the sight of all the people upon mount Sinai.
This is the moment when the covenant was proposed and agreed to by Israel. 3 days before the voice at Mt. Sinai.
Notice from this passage that no commands or laws were given to Israel just yet. This covenant wasn't "The Law" but an agreement "to obey whatever Yah tells Israel to do", this is why it had to be agreed to
first before any law was given. The moment they agreed they would be bound to obey ANYTHING Yah commands of them, at any point.
So say he told them to kneel for 30 secs every Monday, they were bound to obey. But let's say he changed this command later on and told them to jump for 20 minutes every Monday instead, they were still bound to obey. Then let's say he changed the command back to the original kneeling years later, they still were bound to obey because of the covenant. Such changes in commands don't nullify the "covenant of obedience" Israel has with Yah's because it's based on them obeying, not on which laws were given to them to obey. See what I mean?
Let me try to illustrate it visually through text:
Obey me Israel...
kneel for 30 secs > now jump for 20 minutes > now back to kneeling for 30 secs
Obey me Israel...
Follow these commands > now do these Levitical works also > now back to following just these commands
So the covenant that was proposed was a "covenant of obedience" between Israel and Yah, with the purpose being Israel would become a treasured
kingdom of priests (i.e. a priest kingdom). Notice the phrase "kingdom of priests" in the passage above. There was never supposed to be just priests from Levi in this covenant.
...But Israel disobeyed the first set of commands...
So Yah commanded them further to perform the undesirable animal rites (until they could be forgiven), saying "
By disobeying my commands you're in violation of our agreement. I have every right to kill you, so you had better obey this (sacrifice) law if you don't want to die" (I'm paraphrasing). The tribe of levi then received the right to be the personal possession Yah promised to
the whole nation because they were the only group who sided with Yah when Moses caught the people disobeying, so they reaped the benefits of the promise of set-apart priesthood.
Then after Christ and forgiveness/salvation/restoration, the undesirable animal rites are no longer required and the levitical priesthood is no longer applicable because the original promise was now restored, so this necessitates a law change because elements are obsolete. Now ALL tribes of Israel could once again be Yah's kingdom of priests to the world...and with the promise of the Holy Spirit (i.e. the new covenant) they'd now have the fear of Yah and ability to obey him and never again violate the covenant made at Mt. Sinai.
Mt. Sinai - A kingdom of priests. Priest kings.
So the Melchizedek priesthood wasn't part of the Abrahamic covenant but was specifically the purpose of the covenant at Mt. Sinai. Yah has only covenanted with Israel to be a kingdom of priests, no one else. Gentile believers in Christ are being grafted into Israel right now. Then when Israel awakens from its blindness and is regathered, ALL of Israel (jew and gentile branches) is purposed to take the knowledge of Yah to the world (Romans 11:1-30)...this is why for now Yah has subjected the world to its current emptiness & futility. He's letting the world operate however it wants to until the children of Yah are manifested (Romans 8:20). Yah has an order to his plan and he will do all that he has purposed to do.
Jeremiah 31:35-37
35 Thus saith the Lord, which gives the sun for a light by day, and the ordinances of the moon and of the stars for a light by night, which divides the sea when the waves thereof roar; Yah of hosts is his name:
36 If those ordinances depart from before me, saith the Lord, then the seed of Israel also shall cease from being a nation before me for ever.
37 Thus saith the Lord; If heaven above can be measured, and the foundations of the earth searched out beneath, I will also cast off all the seed of Israel for all that they have done, saith the Lord.
Israel hasn't been replaced.
(Sorry. I think I went on a tangent towards the end, but it's hard not to because it's all connected.)