Rashi on 17b explains that
a) the reason there are so many pallbearers is that "all want to have a share in this merit"
b) those who have already carried the bier must recite Shema even if they are still 'needed' since they have already fulfilled their responsibility to the dead
c) they are all exempt from prayer since it is rabbinical. He then quotes an explanation from his teachers that there is time after the funeral but rejects it as not being an exemption at all
The Gemara on 19a quotes a Braisa that we do not bring out a body to be buried close to time of reading the Shema unless it is a distinguished individual.
Would this Gemara be the case described by Rashi? After all, there are many funerals. Only a distinguished funeral could claim mass attendance, a constant stream of replacement pallbearers, and a timing that would interfere with the Shema but not with prayer.
S. Meer, Chicago, USA
If the Gemara had felt that only in the case of an important person the Mishnah applies, it would have asked from the Mishnah on the Beraisa and then answered that the Mishnah refers to an important person. Since the Gemara asked from the case of Rav Yosef and not from the Mishnah, it would seem that the Mishnah was not a case of a distinguished person's funeral and did not contradict the Beraisa. It is simply describing a situation where the funeral started well before Zman Keri'as Shema and then Keri'as Shema arrived, leaving the pallbearers pondering whether they are obligated. The Mishnah then says that if they have already carried the bier they must recite Shema but are exempt from prayer.
Alternatively, our Mishnah is discussing your case but the Gemara does not ask from the Mishnah as it seems to be talking about a de facto situation where they already buried the dead person, while the Beraisa is talking l'Chatchilah. The Gemara then asks why even l'Chatchilah they buried Rav Yosef at the time of Keri'as Shema and answers that for an important person even l'Chatchilah we can defer Keri'as Shema.
Yoel Domb