If one really believes in Yeshua as being what the Letter to the Hebrews says of him, I think him being Kohen haGadol in the order of Malchizedek - (who wasn't a Levite because in terms of time he came much before him, in Genesis chapter 14 - he blessed Abraham - the book of Jasher says this is Shem, Noach's son) takes care of the issue.
~actually Paul's deliberation of "Melcheitzedek" concept in the book of Hebrews is confusing to the uninitiated in the Jewish midrash. however, let it be so, that the miraculous encounter of Avrahom avinu with that priest (from the order of nowhere) should leave us to rely solely on Avrahom's response to the event. it was more of an epiphany from Above, a priesthood that preceeded the kohanim, a kingly one, and from G-d. of these qualities only Moshiach can fit into. of this event, like Avrahom avinu, we are only left with one type of response: that is, *faith*.
If Yeshua is Son of YHWH, as I believe he is, doesn't it seem silly to split hairs about rabbinic law?
~well, you may dispense with rabbinic relevance if you will. but mind you, outside rabbinic literature there is no other academic light that can aid one's understanding of that brief supernatural encounter of "Melcheitzadek" narrated in the book of Genesis.
Some have made the point that when John the Baptist baptized Yeshua he in effect 1) Levitically declared him a valid sacrifice, and 2) passed High Priestly authority from the Levites (John was a Levite) to Yeshua.
~Yeshua has the *blood* of Levi by way of Miriam and Yosef. He did not need others to confer it him in any manner.
With Yeshua's sacrifice on the execution stake the priesthood changed forever because animal sacrifices were no longer to be done. In the current era, Yeshua is kohen haGadol.
~just the way Paul expounds it, yes He is.
I think we can find the answer if we can prove through the Tana"k that the divine throne was inherited and was not transferred because of the flesh and blood of the father, because to an adopted child all the rights of inheritance was transferred to him.
In the same way happended with the Israelites sons of David who sat on the throne, because in the beginning was God who reigned, but the people rejected him as king, and obviously the heir to the throne had to be his child, by this reason the only way that the descendants of David could sit on the throne of God, was that God adopt them as his childs, and that is why Psalm 2:7 was read at the coronation of the king, for God adopted the descendant of David to be his child in order that he could sit in his throne. (sorry my english).