There is in fact quite a bit of discussion among the Poskim, and various opinions, about whether one is obliged to stand while reciting the Korbanos.

1. The Magen Avraham (OC 48) cites your logic in the name of the Emek Berachah (father of the Shelah, who is cited often by the Magen Avraham - Meyer Lieber ) and writes that one should stand when reciting the Korbanos in the same way that the Kohen was required to stand while offering the Korbanos. This is the ruling of the Magen Avraham.

2. Several Acharonim disagree with the Magen Avraham.

The "Mor u'Ketzi'ah" (of Rav Yakov Emden) records the ruling of the Magen Avraham, but he writes that he did not see his father (the Chacham Tzvi of Amsterdam) stand during the recitation of Korbanos. Rather, the Chacham Tzvi always sat down when saying Korbanos before Minchah. The Mor u'Ketzi'ah states that he does not know what his father's reasoning was, but he writes that it seems to him that in fact there is no good reason to require standing.

3. He explains this as follows. The Gemara in Berachos (26b) teaches that the Chachamim instituted the three daily Shemoneh Esreh prayers to correspond to the sacrifices offered in the Beis ha'Mikdash. This shows that that the prayers are in place of the Korbanos, which we no longer have the privilege to offer in the Beis ha'Mikdash. The fact that the prayers correspond to the Korbanos has Halachic ramifications. For example, the Shulchan Aruch (OC 98:4) rules that one should designate a fixed place for his prayers, just as every Korban had its fixed place in the Beis ha'Mikdash.

4. In contrast, we do not find that there are similar Halachos concerning the recitation of Korbanos, and in fact the practice to recite the Korbanmos is not mentioned at all in the Gemara. One must say, therefore, that reciting Korbanmos is merely to remember the sacrifices that we used to offer in the Beis ha'Mikdash, but one cannot say that it is in place of the Korbanos. It is impossible to compare even in the smallest way our recitation of the verses of the Korbanos to the actual Avodah of the Kohanim. The Chachamim were aware that once the Beis ha'Mmikdash was destroyed, it became imposssible to replace the service merely by saying the words of the Korbanos. On the other hand, the Tefilos do serve, in some way, in place of the Korbanos, but only the Chachamim were capable of understanding how the Tefilos can serve in place of the Korbanos.

5. When the Chachamim, after the completion of the Gemara, instituted the recitation of the verses of the Korbanos in the daily prayer service, their intention was to fulfill the dictum, as expressed by the Gemara in Menachos (110a), that "he who occupies himself with the laws of Chatas is considered as though he offered a Korban Chatas." When we learn about the Korbanos we are rewarded for our good intentions in the same way as we would be rewarded in the Beis ha'Mikdash for actually offering them. Reciting the verses is like learning Torah, and just as one would not say that one who learns Maseches Zevachim must stand up, one is not obligated to stand up when reciting Korbanos.

6. The Tevu'os Shor (#12, printed at the end of Sefer Tevu'os Shor) also disagrees with the Magen Avraham and writes that the Tur and the Poskim who follow him did not write any conditions for the recitation of Korbanos, and the only Posek who writes that it should be said while standing is the Emek ha'Berachah. The Tevu'os Shor writes that he never saw anyone who followed this opinion.

7. However, the Pri Megadim (Eshel Avraham, OC 48) cites the Tevu'os Shor but adds that this applies to the passages recited for other Korbanos, but it is nevertheless appropriate to stand while saying the Parshah of the Tamid, the daily communal offering. The Mishnah Berurah also rules that one should stand up while saying the Parshah of the Tamid.

Kol Tuv,

Dovid Bloom