The author of Sheilas Shalom on Sheiltos gives this issue an adequate dissertation. He establishes Rashbam’s opinion that this is indeed the Rav Achai of the Savorai, which was added in after the sealing of the Talmud. He deflects Rabeinu Tams logic (cf. Tosafos, Zevachim 102b, s.v. parich) by pointing out that the same order is found in Nidah (33a), where Rav Asi, an earlier figure, also answers Rav Achai’s question. He explains based on Tosafos (Chulin, s.v. anah) that the question was already asked in the earlier Amoraic times, but it was also asked later by Rav Achai. Read further for more discussion.
This is also the apparent opinion of Maharatz Chajas in Mavo Hatalmud (31).
Rabeinu Tam’s rule is thus no longer valid, because the only reason that Rav Achai has his own word is indeed because it was added in later, as Rashbam notes.
As far as the rule then stated regarding specific phraseology among Amoraic statements, it is possible to now decrease the intensity in which Rabeinu Tam was quoted, and to say that he was only quoting analogous examples to explain his position on Rav Achai. However, he would perhaps concede.
[In a similar vain, perhaps Rabeinu Tam’s rule can be used to further explain the words of Rashi in Nidah (26a, s.v. aimah).
Additionally, to perhaps lighten your case concerning the usage of Rabeinu Tam’s specific phraseology among other Amoraic statements, it can be postulated that indeed the Amora himself had done such an action. For example, in Nidah (14a, top) where R. Yehoshua Ben Levi is actually demonstrating his stance against those who commit certain nefarious actions. This is the opposite of what you write, “Therefore the amoraim were not using these words themselves”.
It is thus different because it is recounting term rather than a dialectic term. Although this really calls into question Rabeinu Tam’s whole methodology of comparisons, which is why I leave this in brackets.]