This is a very interesting and observant question!

1) I think that a key to answering the question may be to point out that actually this is not really an Agadeta Rashi, but rather Rashi is telling us a Halachah about why the Beis ha'Mikdash was not built in Ein Eitam. Rashi writes that it could not have been built in Ein Eitam because the part of the Beis ha'Mikdash which must be in the portion of Yehudah would be too far away from the part which is in the portion of Binyamin. Rashi writes that we require that it be possible to have the Lishkas ha'Gazis, the area of the Beis ha'Mikdash where Halachic rulings were established and therefore is associated with Yehudah, located near the Azarah, which is where they brought the Korbanos, and was partly in the portion of Binyamin.

2) Therefore, when Rashi writes that we require "v'Kamta v'Alisa" he means that the latter Pasuk is teaching that we have a Mitzvah to go up to the Beis ha'Mikdash every time we have a difficult question in Halachah. If you look at the context of the verse, you will see that it is talking about a Halachic dispute which requires a Halachic solution.

3) We also notice that there is a big difference between our Rashi and the Midrash Tanchuma. Our Rashi is not discussing at all the three different Batei Din that sat in the Beis ha'Mikdash. In contrast, the whole purpose of the Midrash Tanchuma is to cite three different phrases in the verse in Parshas Chukas which correspond to the three different Batei Din. In fact, the Sifri that you cited (to Devarim 17:9) is also discussing the three Batei Din (which are also mentioned in the Mishnah in Sanhedrin 86b). In my opinion, Rashi in Zevachim is not directly connected to the Sifri. The Pasuk "v'Kamta v'Alisa" is actually an explicit Pasuk stating that one must go up to the place where the Din is done, and from this we learn that the Lishkas ha'Gazis must be near the Azarah. We do not need the Sifri to tell us this. The Midrash Tanchuma is not telling us a Halachah, but rather it is a Derashah about the Madreiga of the three Batei Din that existed in the Beis ha'Mikdash and this was foreseen in the Shiras ha'Be'er in Parshas Chukas.

5) In short, Rashi does not cite either the Sifri or the Midrash Tanchuma because they are talking about the three Batei Din, while Rashi is talking about a more basic point, that the place where one goes up to for Halachic rulings must be in a high place in the Beis ha'Mikdash which is the Azarah, and is learned from an explicit Pasuk; Rashi is not going into the question of exactly where the three Batei Din were.

6) Looking more into this matter, it seems to me that, to be more precise, Rashi is not learning from "v'Kamta v'Alisa" but rather from the continuation of that verse, "El ha'Makom" -- "to the place." The Torah tells us that for a Din Torah (of a sufficiently severe nature, of course) we must go up to the Beis ha'Mikdash. The Gemara in Sanhedrin (14b) derives from this Halachah that "Melamed sheha'Makom Gorem" -- it teaches us that the place where the Sanhedrin is situated is the cause of their ability to issue Halachic rulings. Even if the Sanhedrin had been moved slightly to Beis Pagi (which is a place inside the walls of Yerusahalyim and has the status of Yerushalayim for all other purposes, -Rashi), this place is invalid for the Sanhedrin. Tosofos in Avodah Zarah (8b, DH Melamed) writes that the Sanhedrin must be near the Shechinah, and even Har ha'Bayis is not sufficently near.

So when Rashi here in Zevachim (54b, DH v'Ika) writes "v'Kamta v'Alisa" we must notice that he also writes "v'Go'" -- "etc." The "etc." is very important here, because Rashi is referring to the continuation of the verse, that the Sanhedrin must be in "the place." Rashi is not referring either to the Sifri or to the Midrash Tanchuma, but rather he is referring to Sanhedrin 14b and Avodah Zarah 8b that "Melamed sheha'Makom Gorem."

Kol Tuv,

Dovid Bloom