[William Cloud Hicklin]

one would have to assume that Ingwe must either be identical with the first unbegotten Elf, Imin, or at least be of his line because else it would be difficult to explain how Ingwe could usurp or rise to the kingship of the Vanyar (and, in fact, all the other Elves) if he was just some random elf who ended up traveling with Orome to Aman.

That doesn't necessarily follow. We know that Elves who had been in Aman were physically and mentally enhanced, very obvious and perceptible traits emphasized at various points early in the LR as well as the Silmarillion. Elwe, Finwe and Ingwe might well have been "just random Elves" with the stones to accept Orome's rather daunting proposition, but when they returned they would have been perceived immediately as "a cut above." Still, given Tolkien's predeliction for noble lineages I venture that if asked he would put those three in the hereditary lines of Imin etc.