Well put. Karaites are rare. There's probably only about 50, 000 worldwide, if that. They are generally accepted as Jews, although outsiders may not see them as Jews (Nazis didn't, interestingly enough). There are a couple out there.
Another interesting example is that the Greek Jews use the Jerusalem Talmud, as opposed to the Babylonian Talmud.
But as rmlew said, if you believe Jesus was the son of G-d, or the Messiah, you are a Christian. Which is fine and good, but it's not the same as being a Jew.
Judaism's beliefs are very clearly laid out, and given there aren't that many of us anyways, and it's pretty flexible in terms of orthodoxy, the official branches just basically are classified by degree of orthodoxy.
A Jew is anyone born of a Jewish mother or Halakhically converted to Judaism, regardless of belief or lack of it. If atheists, b*ddhists, and pagans can be Halakhically Jewish I see no reason why that adjective should be denied to "Hebrew chr*stians."
I am aware of all the other things you said. However, my point was that Qara'im and other small-o "orthodox" heresies are never included in the "branches of Judaism," which always consist of Orthodoxy smothered by liberals.
I once met a young man who believed the Written Torah was from Heaven but who rejected the rest of the Bible (as well as the Oral Torah) and even rejected the doctrine of an afterlife. While he certainly was not an Orthodox Jew, I fail to see why his belief system failed to qualify as a "branch of Judaism" just as much as "reform," "reconstructionism," and "secular humanistic Judaism."
I am not a chr*stian and I do not accept "Jews for J*sus" as orthodox Jews. I merely point out that being born of a Jewish mother makes one a Jew according to Halakhah, and to make apostasy to chr*stianity the one and only occasion when a Jew is "declassified" is not only hypocritical but feeds anti-Semitic stereotypes about "Jews not caring what you believe so long as you are not a chr*stian."
I am afraid that Jews will never understand why Fundamentalist chr*stians cannot see the parallel between Jews for J*sus and chr*stians for Mohammed. The Fundamentalist Protestant notion of Judaism and chr*stianity being in fact a single religion (with chr*stians as "completed Jews," G-d forbid) stems from the Protestant Bible. Because the only thing that separates the TaNa"KH from the "new testament" is the turn of a few pages, because the Bible has no commentary printed with it to explain anything, because this is the only bible the Fundamentalist Protestant has ever known, he simply cannot fathom the idea that the "new testament" doesn't really belong. He deals with the contradictions between "the two testaments" with the same attitude that devout Jews have with regard to "contradictions" between the Sages: 'Ellue va'ellu divrei-'Eloqim Chayyim. Chr*stians are "completed Jews" because they have the "completed Bible." "Why did you people tear the "new testament" out, anyway?" [/sarcasm]
Fundamentalist Protestants do not understand the comparsion with moslems being "completed chr*stians" because Mohammed didn't tack the koran onto the chr*stian bible to "complete it." If he had, all these "Bible-believing chr*stians" might be "bible-believing moslems" today.