The end of the permissible time for Isha prayer

It has been narrated to us from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: "The time of Isha is until Fajr." And it is reported from him and from Sayyiduna Abd al-Rahman bin Awf (may Allah be pleased with him), concerning a woman who becomes pure (from menstruation) before the dawn breaks, that she is to pray Maghrib and Isha. And it is reported from Ubayd bin Jurayj that he asked Sayyiduna Abu Hurayrah (may Allah be pleased with him): "What is the last time of the Isha prayer?" He said: "The breaking of the dawn."
And it has been narrated to us from Sayyidah Aishah (may Allah be pleased with her) that she said: One night the Messenger of Allah (peace and blessings be upon him) delayed the Isha prayer so much that most of the night passed and the people of the mosque fell asleep; then he (peace and blessings be upon him) came out to them and led them in prayer, and said: "Indeed, this is its (true) time, were it not that I fear placing hardship on my Ummah." And this comes in the chapter on delaying the Isha prayer.

Sayyiduna Abu Qatadah (may Allah be pleased with him) reports from the Prophet (peace and blessings be upon him), in a long hadith, in which it is: "There is no negligence in sleep; negligence is only on the part of one who does not pray the prayer until the time of the next one comes."