Interesting thought, though I get the idea that in offering this suggestion you are only playing "devil's advocate" and that you ascribe to neither school of thought.
At the risk of detracting attention from the arguments and evidence to my own faith or lack thereof, I am agnostic with a "spiritual side", who is sincerely interested in the history of the Bible and understand it (or rather, its constituent writings) in its cultural and religious context. Thus, I am equally critical of apologetic claims that I personally believe to be inaccurate or historically incorrect as "atheist" claims that are fallacious or inaccurate (such as my recent postings against the Jesus/Horus/Osiris meme).
But I wasn't merely presenting that option as a "devil's advocate"; it really is a logical option and one that has a place in Christian history, whether it is the belief of copyists engaged in altering the text who view themselves as fixing an already corrupted text, or the Roman Catholic view in the continuing revelation and authority in the church, or even the fundamentaist ideas in the KJV-only movement who regard the English translators as producing a perfected text. And the fundamentalist view that predicates acceptance of Christian belief on inerrancy of the Bible is hardly the only option that Christians have expressed. Some are quite comfortable with their faith in Christ while acknowledging an errant Bible because their faith does not depend on written revelation alone, or they trust the revelation is reliable regardless of whether it is 100% accurate or not. Isn't that what faith is about, after all? It is believing without full assurance where real faith comes into play, as it was in the case of Abraham. It seems to me that there is a weakness of faith in the insistance that the Bible must be 100% accurate (at least in its original form, which unfortunately does not exist for anyone today) or else it cannot be trusted. I'm sure you have seen the view expressed that because God gave his revelation to man, and because man has mediated that revelation, it will always be limited by what man can comprehend and express. The very nature of the text itself limits the revelation. As soon as a person reads anything, the process of (re)-interpretation begins, let alone the pliable nature of the form itself. I think it is best viewed as a witness to God or Christ -- and no witness is infallible. As some have expressed it, the Bible is more like John the Baptist. It points to Christ and tells you all you need to know to find him. But John was imperfect and had his faults and he should not be confused with the one he witnessed about. One does not assume that John had to be infallible and perfect in order to function as a witness. But that is what the notion of inerrancy assumes.
You wrote: Jubilees was not dependent on the LXX per se, as it utilized the Hebrew text directly. The witness to Cainan in Jubilees is evidence that this name was already in the Hebrew prior to its rendering in the Greek LXX. Hmmm. This is not a convincing argument. We have no way of knowing what was and what was not in the Hebrew text that was in front of the author of Jubilees. He may have simply added his "Cainan" material as if he were consulting a Hebrew text after being influenced by the LXX. Or, probably a more likely scenario, he may have then been reading a corrupted Hebrew text containing this second "Cainan" - the same text which was also improperly relied upon by the translators of the LXX.
It is the most probable assessment of the evidence. The textual evidence of Jubilees shows that the author wrote in Hebrew and was dependent on a Hebrew text, not the Greek LXX or even the Egyptian text tradition that it represents. The underlying text had strong affinities with not only the LXX but with the Samaritan Pentateuch (in many cases against the LXX, and never with the MT against both LXX and Sam.), such that the text is of a Palestinian type closely related to Sam. and the Qumran MSS. It has parallels with the LXX against the MT because the Vorlage of the former was derived from the Palestinian text (according to Frank Moore Cross, the Egyptian version of the Hebrew text branched off from the Palestinian text in the fifth-fourth centuries B.C., the Palestinian text arose earlier in the fifth century BC, and the proto-Masoretic Babylonian text which developed independently in the interim was introduced into Palestine in the first century BC, when Masoretic readings began to appear against the Palestinian text type). Compare, for instance, with the findings of James VanderKam on the use of Genesis in the Qumran Genesis Apocryphon (Textual and Critical Studies, pp. 278-279; JBL, 1978); he finds that it attests the same Palestinian text type as Jubilees and where they overlap, they agree with each other 85% of the time. In other words, both texts make very similar decisions in whether to follow the LXX against Sam. or Sam. against the LXX, indicating that they had similar Hebrew versions of Genesis at their disposal. It is a more parsimonious explanation to conclude that the author of Jubilees (which we know from internal evidence probably had a Palestinian provenance) followed a Palestinian Hebrew text of Genesis that resembled the LXX in some places, the Sam. Pentateuch in other places, and both (against the MT) much of the time, and that the author of the Genesis Apocryphon had a similar text at his disposal.
So far as your contention that "the structure of the genealogy itself supports the view that 'Cainan' is original to the genealogy" due to the fact that without this second "Cainan" there are only 76 generations from Adam to Jesus, counting Adam as #1 and Jesus as #76. First of all, who ever said that there had to have been 77 generations from Adam to Jesus? Maybe if the number was 70 (as in the "70 weeks" prophecy) the argument would be a bit more persuasive.
I agree that it is not proof of the originality of "Cainan" in Luke, but it is imho relevant evidence, on account of its internal features and kinship with earlier schematizations of the generations of world history to the eschaton found in the Apocalypse of Weeks (which presume ten weeks of 70 generations, with Enoch at the conclusion of the first week and Abraham at the conclusion of the third week, cf. 1 Enoch 93:3, 5) and the Book of Watchers (which presume 77 generations from Adam). There is a neat pattern in the Lukan genealogy that corresponds to the phases of Israel's history and highlights the coming of Jesus with the names placed at the conclusion of multiples of 7 generations (in a similar fashion to the way that the Apocalypse of Weeks uses the conclusion of weeks to highlight important events in Israel's history). Perhaps the resemblance is coincidental, but I think it more probably indicates that the author of Luke utilized a similar approach toward the descent of Jesus, grouping generations into weeks (with groups of weeks corresponding to phases of Israel's history) and using the sabbaths of a number of the weeks to foreshadow the coming of Jesus.
