1. It seems that in both cases here: on 14A and 15B - the talmud is not previously quoting Rav Yehuda at all, and is in effect quoting the response of Shmuel to Rav Yehuda in another case entirely!
However the only other case does not relate to Rabbi Tarfon and the "Rabbis" but to Rabbi Yishmael and Rabbi Akiva on DAF 36B. Thus it seems that in these two instances the talmud is paraphrasing Shmuel!
So why does the talmud bring this quote from Shmuel?
It seems that the reason is to show us that the Mishna combines Halachot of different origins. This is not exceptionally surprising:after all, Rabbi Yehuda Hanssi put forth this compilation of the older teachings, and in some he agreed with one and in other decisions he agreed with another older opinion, as Rav Nahman says on Beitsa 2A: Who made the Mishna Anonymous - Rabbi [Yehuda]!
And on Horayot 12B and Hulin 84A and Rosh Hashana 7B and Megila 9B Rav Yosef also says the same!
And Rav Zeira on BabaKama 47B "Tavra: the tanna who said this did not say that"
And on Yevamoth 108B Rav Yehuda says that Shmuel also said : "Tavra: the tanna who said this did not say that" - and there and Rabbi Elazar is also quoted as using that phrase.
2. When Shmuel said "Shvok Matni' V'Tta aBatrai" - What can Shmuel have meant? A literal translation could be: "Leave [or Ignore] the Mishna or the Beraita and follow me."?
In the first case (14A) Shmuel could have said only: "Yes, the first clause is according to Rabbi Tarfon and the conclusion is according to the Rabbis", and in the second (15B) "Yes, the first clause is according to the Rabbis and the conclusion is according to Rabbi Tarfon"!?
Could it be that the actual quote of Shmuel is only "Shvok Matni' V'Tta aBatrai", and the rest is the interpretation of the Talmud to Shmuel's expression?
But what does "Shvok Matni' V'Tta aBatrai" really mean?
1. As you mentioned, there are numerous cases where the Gemara answers a Mishnah according to two Tana'im. Therefore I see no reason to say that the Gemara brought Shmuel unless he actually said it on these Mishnayos.
2. Rashi is as real as it comes. He translates "Shvok" as "leave," trying to explain the Mishnah according to one Tana, and "Ta" as "follow me" who explains the Mishnah according to two Tanaim.