1) It is not sufficient if only a small portion of the Shirayim is poured down the Yesod. The words "Iy Akar Lehu l'Gamri" that Rashi uses do not mean that it is only invalid if all of the blood is not spilled on the Yesod. Rather, Rashi means that just as the omission of other Matanos prevent the Kaparah being attained (when they are omitted entirely), the omission of the Shirayim also prevents the Kaparah.

See the Tosfos ha'Rosh who writes that Rashi derives this from the words of the Torah, "v'Kilah mi'Kaper," which imply that one attains Kaparah only if he does "Kilah" -- that is, he must use up everything. This teaches that he must pour all of the Shirayim down the Yesod.

2) Let us attempt to understand the quantities of blood that were received by the Kohanim.

(a) First, the Gemara in Zevachim (35a) tells us that with regard to the atonement acquired by the Korbanos, only the blood through which the soul of the animal departs is considered blood. Therefore, only the blood which flows at the time of the Shechitah must be received by the Kohen.

(b) Second, we should point out that the blood may be received in more than one vessel. This is evident from Zevachim (34b) where the possibility is mentioned of receiving the blood of the Chatas in four vessels. In fact, the Meshech Chochmah (on Vayikra 9:9) writes that each of the four sons of Aharon received the blood of the Chatas in his own separate vessel.

(c) In addition, see Tosfos to Zevachim 34b (DH l'Ime'utei) who writes that the law that all of the blood of the Par should be received is a Mitzvah, but it does not prevent the atonement being attained if one did not do it. It is only a requirement l'Chatchilah, but it is not Me'akev b'Di'eved.

I also found an interesting source relevant to the considerable weight of the blood collected. This is from the Sheyarei Korban, one of the commentators on the Yerushalmi, on the seventh chapter of Yerushalmi Yoma (37a). He refers to the Mishnah in Yoma 53b that according to the Rabanan who disagree with Rebbi Yehudah, there were two gold stands in the Heichal. The Sheyarei Korban writes that the reason why two stands were required is that the Chachamim were concerned that the Kohen Gadol should not become weak ("Chulsha d'Kohen Gadol") as a result of having to carry all of the blood of the cow and the goat at once in his hands.

We learn from this that even though it is only a Mitzvah l'Chatchilah to receive all of the blood, nevertheless they were particular to do this in the Beis ha'Mikdash and made practical arrangements to make this possible.

(d) A bigger Chidush is stated by the Me'iri (to Yoma 32b) who writes that once one has slaughtered the majority of the two Simanim (i.e. the trachea and the esophagus) it is considered that the Avodah of Shechitah has been completed. Even though it is a Mitzvah to complete the Shechitah so that all of the blood should leave properly, nevertheless this is only a Mitzvah d'Rabanan and is not Me'akev.

(e) In the light of the above sources, we may say that the Mizrak was not necessarily so large and heavy. In addition, we should understand that the pouring of the Shirayim onto the Yesod was an Avodah in its own right. In fact, Rav Yosef Dov Solovetchik zt'l writes in his Chidushim to Zevachim 25a (on the Sugya that the Shochet must receive all of the blood) that it is possible that for Korbanos for which there is no Mitzvah of pouring the Shirayim on the Yesod (for example, Bechor, Pesach, and Ma'aser Behemah) there is also no Mitzvah to receive the blood. This suggests that the Mitzvah of pouring the Shirayim is not merely a way of disposing the blood which was not used for the Matanos, but was in fact an Avodah in its own right.

(f) I later posed this question to a Gadol, who replied simply that a large vessel was required to receive the blood from the animals, and in fact the Shi'ur (the size of this vessel) was such that it was large enough to receive all of the blood.

(g) Here is an additional comment on your question concerning the Kavanah behind receiving a large quantity of blood even though only a small amount can be used for Matanos. The Sefas Emes (on Rashi, Zevachim 37a, DH Minayin) writes that even though Rashi there implies that the Mitzvah of pouring the blood on the base of the Mizbe'ach applies only if there is blood leftover after the Matanos have been sprinkled, the words of the Gemara and the Rambam suggest that in fact there is a Mitzvah to make sure that blood remains so that it can be poured on the Yesod. In other words, there is an independent Mitzvah in its own right to pour the Shirayim on the Mizbe'ach, so the Shirayim in fact represent another "offering" offered on the Mizbe'ach, and are not merely something one pours on the Mizbe'ach if it so happens that there is some blood leftover. The Sefas Emes cites an opinion in Tosfos (Zevachim 53b, DH ha'Olah) to this effect; it is clear from the Sugya there that there is a Mitzvah to perform a Matanah of the remaining blood.

(h) I would like to add a source relating to the vessels in which the blood was received from the animals. This is from the Talmud Yerushalmi (Yoma 3:8), based on the verse in Ezra (1:9) which describes the vessels in the second Beis ha'Mikdash at the time it was built. There were 30 gold "Agartel" and 1,000 silver "Agartel." Rebbi Shmuel bar Nachman explained that the word "Agartel" hints to the word "Agar" -- collecting. This indicates that this utensil was used to collect the blood of the goat. Rebbi Shimon ben Lakish explained that the gold Agartel was a utensil used to collect the blood of the cow. I found in a Sefer called, "Karnos ha'Mizbe'ach," which received an approbation from Rebbi Meir Shapira zt'l (the Lubliner Rosh Yeshiva and the founder of the Dafyomi program), im which Rav Shapira writes that the reason why the Agartel used to collect the blood of the goat was made from gold was because "ha'Torah Chasah Al Mamonam Shel Yisrael" -- the Torah cares about the money of the Jewish people. Since the goat has less blood, a smaller vessel is required to receive all of its blood, and it is not so expensive to make this out of gold, while the larger vessel required to receive all the blood of the cow was made of silver.

I would also suggest that the reason why there were 1,000 vessels for the blood of the cow and only 30 for the blood of the goat is that many vessels were necessary in order to collect all of the cow blood, which is a much larger quantity than the goat blood. This fits with what I wrote above reply that we find in the Gemara (see Yoma 57b) that it is possible to collect the blood in four different vessels. The blood of the cow may have been collected in many different vessels, which is why so many Agartel were needed.

I hope I have helped cast some light on your comment that the Mizrak to receive the blood must have been extremely large and heavy. We have now seen that the vessel used to receive the blood of the cow was larger than that which received the goat blood, and in addition there were more vessels available for the cow blood.

Kol Tuv,

Dovid Bloom