Great question,
I have my own original answer based on a saying of the Talmud:
"Kohanim Zerizim Hem" (Priests are possessed of alacrity {in serving Hashem}) (see Talmud Pesachim 36a and many other places). I have seen the term "zerizus" used for "speed". (see Talmud Pesachim 4a: "Zerizim makdimin Lemitzvos"... "A "zariz" will do a mitzvah at its first available time {early}")
However, "Zerizus" when applied to the Kohanim, is not a trait of speed only, but also of being conscientious. It means that Kohanim perform the commandments quickly AND carefully.
For instance, Pesachim 36a says that the Minchah offering may have its flour prepared with lukewarm water. Almost all bread products in the Bes HaMikdash were prepared with the same law as Matzah (it could not be offered leavened). Although lukewarm water may cause the dough to become leavened, the Gemara was not concerned because Kohanim were in charge of the Mikdash and they are "zerizim"; so they will not let the dough become chametz.
So, how did the Kohanim process so many Pesach offerings in the few hours of the afternoon of the 14th of Nissan? The answer is that they were "Zerizim". They not only did the job quickly, but they must have taken steps to insure that time was not wasted at all, so everyone would be able to bring their Korban before time ran out!
A Korban Pesach was designated by the head of a household and that person would then register his family and others to eat from the Korban. (see Shemos:12) Therefore, the 30,000 sheep/goats given in Divre Hayamim (Ⅱ, 35:7–9) for the Yisraelim as Korban Pesach animals, were for thirty thousand GROUPS of people; not individuals.
I am sure that the people of the time did what they could to try and put as many people as possible onto one animal. This was not only to insure that everyone "car-pooled" (thereby reducing the total amount of animals needed to process), but also because any meat of the holy sacrifice should not be left over (and would be burned in the morning - Shmos 12). The more people per animal would reduce waste. So, although we do not know how many people attended above, we do know how many groups there were.
By contrast, the 3000 cattle were assigned as a fixed number for the needs of a certain amount of people. The Chaggigah offering was used with the Pesach as additional meat so the Pesach could be eaten on a full stomach and enhance the holiday. First the Chaggigah was eaten, then the Pesach requirement was eaten on a full stomach. (See Mishnah and Gemara: Pesachim 69b - 70a with Rashi, Tosefos, and others at length for an in depth understanding)
However, the Chaggigah was optional. (see Pesachim 69b) If there were fewer people registered on one Pesach, then there would be enough meat from the Pesach itself per person, so the Chaggigah meat was not needed. Minimally however, we would want that each lamb provide 1 olive volume of meat per registrant.(see Rambam, hilchos Korban Pesach 8:3)
Therefore, the 3000 cattle (and 500 for the Levites and 300 for the Kohanim) were given so they could eat enough meat first, before eating a minimum of Pesach meat. Furthermore, since sheep and goat can be used for the Chaggigah, we see that the exclusive use of cattle may have been for the efficiency of using a larger animal that could be processed faster than many sheep/goats. All of this was done apparently to provide the maximum registration per sheep/goat.
Now, the 2600 Passover lambs/goats for the Kohanim should have been 3000 since the Kohanim needed 300 cattle for back up meat (similar to the other groups (Yisraelim and Leviim) who also were given 10% cattle.) However, since Kohanim are "zerizim", they wanted to process even less animals for the Pesach to save time. They therefore were meticulous and registered more people per lamb/goat among themselves and saved an additional 400 offerings from the busy schedule.
