The Judaism DIR would be the appropriate place. Karaites might be considered heretical, but nobody denies that they are Jews. Orthodox Judaism considers Reform to be heretical, too, and they are in the Judaism DIR.
First of all, there certainly can be questions about Karaites being Jewish: they practice patrilineal descent, and have for many centuries, and thus often intermarry with non-Jewish women. So to the best of my knowledge, most halachists have advised that Rabbinic Jews cannot marry Karaites or use them as halachic witnesses or count them in minyanim, etc., unless it has been verified that their mother and her maternal line have been halachically Jewish for quite a number of generations.
It's true the same problem begins to present itself for Reform Jews, but Reform Judaism has only been practicing patrilineal descent for a few decades, and they also accept matrilineal descent as well, so the problem has not yet gotten to the point where one has to presume that a Reform Jew is not halachically Jewish: one can still safely assume that if a Reform Jew's mother was Jewish, that person is halachically Jewish, and need not ask further (though of course many in the Orthodox world now do just that).
Second of all, Reform Jews technically have not abjured the Oral Torah. Halachically they err in deeming mitzvot d'rabbanan (Rabbinic mitzvot) and certain Rabbinic interpretations of the toledot (unfolding progressions of sub-mitzvot extrapolated from a major mitzvah) optional rather than mandatory. But technically, they do not outright reject that Rabbinic Judaism is authentic Judaism and the teachings of the Rabbis the basis for how to practice Judaism.
Whereas Karaites do abjure the Oral Torah, and completely deny the authority and authenticity of Rabbinic teaching as the basis for how to practice Judaism.
Furthermore, Reform Judaism was begun with what we might call from a traditional standpoint errors of good faith and intention. They wished to better practice Judaism in a modern age, which is good, but made (from a traditional standpoint) errors in their choices as to how to accomplish that. But Karaism was begun with an error born of pride, arrogance, and overweening ambition: Anan ben David, the founder of the Karaite sect, began it not because of deep philosophical motivations, but because of frustrated political ambition. He wanted to be Reish Galuta (Exilarch), was passed over for the office, and blamed the Gaonim (the heads of the two Rabbinic Academies of Babylonia). In a fit of pique, he broke with the Jewish community, rejected the authority of the Gaonim, and in order to do so, rejected the authority of the Rabbis of the Talmud and the Oral Torah they taught, instead claiming to be a revival of the Tzedoki (Sadducee) sect with the virtue of Biblical literalism (despite his new movement's inevitable need to immediately begin interpreting the Torah, since it is unable to be put into practice through strict literalism).
Reform Judaism may be considered heretical by some, but there is still ample reason to include them, and inadequate reason to exclude them. Whether the same will be true in a hundred years is an open question; but for now, it is hard to say otherwise. But if Karaism was ever in the same position, it was over a thousand years ago: their ship has sailed.
So no, I see no reason for them to have a place in the Judaism DIR, since normative Judaism is Rabbinic Judaism. They should certainly have a sub-DIR in the Abrahamic DIR, if they want one. But they don't belong with us any more than Samaritans would, or Messianic Judaism.
