Well I guess I mean I don't think there is any interpolation. I think this is correct:
To the contrary, the entire argument of the epistle depends upon both of these points. Melchizedek has to lack a recorded genealogy (or at least it helps our author's case that he lacks a recorded genealogy) so as to inaugurate a priesthood which does not rely upon genealogical descent, precisely in order that the Judahite Christ might be a priest of some kind (= a priest after the order of Melchizedek).
It's clear that the writer puts Jesus on earth:
7 During the days of Jesus’ life on earth, he offered up prayers and petitions with fervent cries and tears to the one who could save him from death, and he was heard because of his reverent submission. 8 Son though he was, he learned obedience from what he suffered 9 and, once made perfect, he became the source of eternal salvation for all who obey him 10 and was designated by God to be high priest in the order of Melchizedek.
But he is still unborn. He "came to earth", he descended to earth from heaven, as the writer describes elsewhere. But his sacrifice took place in heaven as well. He existed in heaven, unborn, without mother or father, he descended to earth where he suffered, then he ascended to heaven where to underwent a sacrifice.
That he came through the tribe of Judah is merely a reference to his Davidic lineage, which is derived from Pauline teaching.