The Beis Halevi explains the Tosfos Yeshonim that there is a distinction between pesach and other korbonos. Pesach, there is an obligation on the individual and he is required to eat a kezayis. By the other korbonos, the mitzva is that the korban should be eaten, and if accumulatively the korban was eaten, even though there was no kohen who had a kezayis, that is sufficient.
According to the Beis Halevi, we do not understand why the righteous ones held back from eating when it was only the size of a bean, as long as everyone ate the entire lechem hapanim, the mitzva would be fulfilled?
avrohom adler, cleveland, usa
It seems that Beis ha'Levi 1:2:7 understands Tosfos Yeshanim 39a DH SHE'MAGIO as follows. Since the Lechem ha'Panim would anyway be eaten completely by the greedy Kohanim, it follows that the basic Mitzvah of eating Kodashim would always be fulfilled, as B.H. writes that there is no Mitzvah at all on any particular person to eat Kodashim but rather merely that the Kodashim should be eaten, no matter by whom. This way, by the modest Kohanim, B.H. writes that someone who possesses Kodashim is entitled to give it to someone else to eat and the Mitzvah is thereby fulfilled through this. Therefore, even though the greedy Kohanim ate less than a Kezayis of the Lechem ha'Panim, the Mitzvah was still fulfilled adequately this way by the modest Kohanim.
However, if the modest Kohanim would be satisfied by eating the Lechem ha'Panim, they therefore felt it was preferable to do the Mitzvah themselves rather than leave it to others. This is what Tosfos Yeshanim means when he writes "Ki Dimu" to fulfil the Mitzvah of eating, which can be translated "They wanted to do something similar to the Mitzvah", i.e. even though the basic Mitzvah would be performed without their participation, nevertheless if they could do a complete Mitzvah of eating, i.e. by being satisfied, which is the best kind of eating, then it was better to take part rather than leave everything to others. On the other hand when there was only a bean-size and they were not satisfied, T.Y. writes there was no Mitzvah "Le-Gamri" i.e. no Mitzvah at all, because the modest Kohanim were not satisfied and therefore did not perform a complete Mitzvah of eating and consequently the Mitzvah could be done just as well by the greedy.
(See also RITVA who writes something similar to the above - if there was a blessing in the eating of the modest, they would not refrain from this because this did involve an element of a Mitzvah. See also MAHARATZ CHAYES here and TESHUVAS CHASAM SOFER OC 49.)