Since the commenter named Stuart never got back to me about Rabbi Reisman's shiur (Corection: I just got it after this post went up), I did further investigation on my own to satisfy my curiosity.
Please note: all translations are mine, since the sources I saw were in Hebrew. Thus, any inaccuracies are also mine.
I checked the Toras Chaim edition of Bereishis (actually, the 2nd volume of Bereishis) and found that the Chizkuni writes:
Umilvad Neshei Bnei Yaakov: This comes to exclude the twins, that they were not included in the count, behold you have sixty-six.
Then I went to the big Mikra'os Gedolos HaMefoar and found that the Sifsei Chaim quotes the Maharshal in order to explain the words in Rashi "shemeisu lifnei yeridasan l'mitztraim - that they died before they went down to Egypt:"
Since if you don't say that, why are they not counted with the other children? And therefore [Rashi] says that they died and these wives were nochriyos [foreigners] that are not included in those that came from the thigh of Yaakov, and the verse is explained from its own reason.
Finally, I saw the Ramban that Rav Moshe Feinstein referenced in the Darash Moshe:
Rabbeinu Shlomo wrote, "and according to the one who says twins were born with the shevatim, we need to say that they died before they went down to Egypt since they are not counted here."
But we don't need this, because it says in Bereishis Rabba 4:21, "Rabbi Yehuda said the shevatim married their sisters," and behold these twins were the wives of the sons, and the posuk says in reference to them, "except for the wives of the sons of Yaakov." And according to Rabbi Yehuda from this the verse says as it does, because what's the reason to say "except for the wives of the sons of Yaakov" who were Canaanites, since it already said "that came from his thigh?" It's only because these wives of his sons were also from those "that came from his thigh" that it says this. But, [the verse] didn't publicize them here, just as they were not mentioned at the time of their births with the shevatim.
And further, it only mentions those that had children and multiplied in Egypt, to inform us of the big miracle that happened with the great multiplying that happened in Egypt, and those [involved] in this are seventy souls, and their wives were not counted because a man and his wife are one.
So there you have it - boruch shekivanti! While I am at peace with the likelihood that these twin daughters were alive and well, I still wonder why Rashi thought of his understanding instead of the Ramban's, which just seems a bit more in alignment with the psukim...