How can the Hadith that Christians will be the most numerous people on Earth in the End Times be reconciled with the conquest of Rome?

Imam Ahmad narrated from Abdullah ibn Amr ibn al-Aas (may Allah be pleased with them both) that the Prophet (peace and blessings of Allah be upon him) said that the city of Heraclius (Constantinople) would be opened first. This does not contradict the hadith, "The Hour will be established while the Byzantines are the majority of people," for their large numbers do not prevent the conquest of their lands. Perhaps they will embrace Islam and participate in the Islamic conquests, as Ibn Kathir mentioned that the Byzantines may embrace Islam at the end of time and conquer Constantinople. As for the Hour being established upon them while they are disbelievers, this is possible because the Hour will be established upon the worst of people.