I found a few other references that presuppose the generation of "Cainan".
(1) In addition to the legendary discussion of Cainan in ch. 8, Jubilees elsewhere states that "there were twenty-two chief men from Adam until Jacob" (2:23), and this is the case only if Cainan is included as the twelfth generation from Adam.
(2) Jubilees is otherwise dependent on Enochic traditions (see especially Jubilees 4:16-26), and the Apocalypse of Weeks (from the mid-second century BC) designates Enoch as the "seventh" generation in the first week (1 Enoch 93:3), such that each "week" consists of seven generations. Thus, 1 Enoch 93:4 dates the Flood "within the second week" (i.e. the generation of Shem, the 4th generation of the second week), v. 5 dates the generation of Abraham to the conclusion of the third week (i.e. the 7th generation of the third week), v. 6 dates the giving of the Law to the conclusion of the fourth week (i.e. the 7th generation of the fourth week), and v. 7 dates the building of the Temple to the completion of the fifth week. This scheme also presupposes the generation of Cainan, as its insertion would make Abraham the 21st generation, i.e. the 7th generation of the third week. Without Cainan, Abraham would be the penultimate generation of the third week -- not the last generation. It is the same situation with the timing of the giving of the Law to Moses. 1 Chronicles 6:1-3 indicates that Moses, Miriam, and Aaron were the great-grandchildren of Levi (i.e. Levi > Kohath > Amram > Moses), and by the time the Law was given, Moses already had children of his own (Exodus 2:22). So that would mean that the Law was given in the 4th generation from Levi. If we count the generations with Cainan included, Levi would be the 24th generation, and four more generations would bring us to the 28th, the last generation of the "fourth week" (4 x 7 = 28). Without Cainan, this scheme wouldn't work. This apocalyptic orientation of the scheme is that there would be a total of 10 weeks, or 70 generations until Judgment Day (at the conclusion of the 70th week, cf. 91:15). This is related to the notion in the Book of Watchers that the fallen angels would be bound for 70 generations until Judgment Day (1 Enoch 10:12), although this reckons the start of the 70 generations from the time of Enoch, rather than creation. This amounts to a total of 77 generations until judgement is concluded.
(3) The Enochic generation scheme is separately used by the Pseudo-Clementine Recognitions in its survey of history from creation to the coming of Jesus, and the Pseudo-Clementine use of 1 Enoch is elsewhere well-attested (cf. especially Rec. 1.29, Hom. 8.10-20). In Rec. 1.29, the fallen angels marry women in the 8th generation, and this corresponds to the generation of Methuselah, i.e. the lifetime of Enoch after he fathered Methuselah and when he interceded with the fallen angels. Then, we read that the sons of men "began to multiply in the twelfth generation" (1.30), and this matches with the generation of Arpachshad. Abraham then was born in the 21st generation: "In the twenty-first generation there was a certain wise man, of the race of those who were expelled, of the family of Noah's eldest son, by the name of Abraham, from whom our Hebrew nation is derived" (1.32). This conforms exactly with the scheme in the Apocalypse of Weeks.
(4) This raises the question of whether the genealogy in Luke follows a similar scheme, and in fact it does indeed appear to do so. If we included the "Cainan" generation, it makes Jesus the 77th generation from the first member of the genealogy, God (Luke 3:38). Counting from Adam, the 77th generation would then be the generation AFTER Jesus, and this fits very well with the first-century apocalyptic expectation that Judgment Day would occur within the lifetime of those who saw Jesus (cf. Mark 8:38-9:1, 13:30, 14:62). Not only is there a coincidental correspondence between the 77 generations of Luke and the 77 generations of 1 Enoch, but the internal structure of the list reflects the use of 7 and 11 (the base denominators of 77) as structuring elements. Thus, Noah is the 11th generation, Abraham is the 22nd generation (11 x 2), Moses (= contemporary of Ram) is the 28th generation (7 x 4), David is the 35th generation (7 x 5), the first Joseph is the 42nd generation (7 x 5), the second Joseph is the 70th generation (7 x 10), and the third Joseph of course begets the 77th generation (7 x 11). And reckoning from Adam, there are also 7 x 3 generations from Adam to Abraham, 7 x 3 generations from Isaac to David, 7 x 2 generations from Nathan to Shelathiel (the exilic generation), and then 7 x 3 generations for the post-exilic era from Zerubabbel to Jesus. So this may support the view that "Cainan" is original to Luke. However the variant textual tradition of the Lukan genealogy (see below) as a whole leaves the question somewhat open.
That leaves the question of P 75 , and from what I have found, this is somewhat uncertain because the relevant portion of Luke 3:36 falls right into a lacuna in the text:
TOU[RAGA]UTOUF[ALEK]TOU[EBER]
T]OU[SALATOUA]RFA[XADTO]U[SHM]
TOUNWETOU]LAMECTOUMA[QOUSA]
So it is possible that "Shelah" dropped out instead of "Cainan", although this seems less likely. More important is the early evidence of variant text tradition of Luke 3:23-28 in Irenaeus who wrote around the same time this fragment is paleographically dated (i.e. the late second to early third century AD). He wrote that "Luke shows that the genealogy which is from the generation of our Lord all the way to Adam contains 72 generations, connecting the end with the beginning" (Adversus Haereses, 3.22.3). This means that more names than "Cainan" were missing in his copy of Luke, and indeed we find many places in the genealogy where names are eventually added (such as another "Jacob" in D at 3:23, or "Admin" in other MSS. at v. 33) or removed (such as in some Latin MSS, which have 72 generations) in the textual tradition.
So this suggests that a missing Cainan or Shelah in P 75 is not unexpected for a late second century date. The presence of "Cainan" in P 4 (third century AD), i.e. TOUFAL[EKTO]UEBER TOUSAL[ATO]UKA[I]N[AM], also shows that this variant was nearly as early in the extant texts. The accuracy argument is problematic because tedious "begat" lists are especially prone to errors, as the textual tradition of the Lukan genealogy itself attests, so it is not implausible that even a careful copyist could have erred (as every other word in the list was TOU, so a scribe copying letter-by-letter could have still settled on the wrong TOU between strokes). More likely in this case, the omission occurred in the parent manuscript that the scribe was copying. No matter how careful, a scribe would not be able to copy something that was already deleted.