ElderofZiyon has now a great catch on this, "It appears that the Al Aqsa Mosque was not considered the third holiest spot in Islam until the 20th century.":
According to A Dictionary of Islam: Being a Cyclopædia of the Doctrines, Rites, Ceremonies, and Customs, Together with the Technical and Theological Terms, of the Muhammadan Religion by Thomas Patrick Hughes (1885):
MASJIDU 'T-TAQWA. Lit. "The Mosque of Piety." The mosque at Quba', a place about three miles south-east of al-Madinah. It was here that it is said that the Prophet's camel, alQaswa rested on its way from Makkah to alMadinah, on the occasion of the Flight. And when Muhammad desired the Companions to mount the camel, Abu Bakr and • Umar did so, but she still remained on the ground; but when 'Ali obeyed the order, she arose. Here the Prophet decided to erect a place for prayer. It was the first mosque erected in Islam. Muhammad laid the first brick, and with an iron javelin marked out the direction for prayer. The Prophet, during his residence at al-Madinah, used to visit it once a week on foot, and he always made a point of praying there the morning prayer on the 17th of Ramazan. A prayer in the mosque of Quba' is said to be equal in merit to a Lesser Pilgrimage to Makkah, and the place itself bears rank after the mosques of Makkah and alMadinah and before that of Jerusalem. It was originally a square building of very small size, but the Khalifah 'Usman enlarged it. Sultan 'Abdu '1-Hamid rebuilt the place, but it has no pretensions to grandeur. (See Burton's Pilgrimage, vol. i. p. 890;)
As for Al-Aqsa?
Surat At-Tawbah (The Repentance) - سورة التوبة 9:108
لَا تَقُمْ فِيهِ أَبَدًا ۚ لَّمَسْجِدٌ أُسِّسَ عَلَى التَّقْوَىٰ مِنْ أَوَّلِ يَوْمٍ أَحَقُّ أَن تَقُومَ فِيهِ ۚ فِيهِ رِجَالٌ يُحِبُّونَ أَن يَتَطَهَّرُوا ۚ وَاللَّهُ يُحِبُّ الْمُطَّهِّرِينَ
Do not stand [for prayer] within it - ever. A mosque founded on righteousness from the first day is more worthy for you to stand in.
Oh, and as for this:
“There is no Temple Mount,” shouted Zahalka. “There is only the Aksa Mosque, I don’t see a Temple Mount, it’s something virtual” he shouted, and continued to call out “al-Aksa” every time anyone in the hearing said the words “Temple Mount.”
Someone might say 'there'll be no Al-Aqsa'.