The short answer is no, there isn't any published information as to what he may have considered the ending of each Age. Tolkien was even relatively inconsistent on the time elapsed since the events of the Lord of the Rings, as in History of Middle Earth he noted:
The moons and suns are worked out according to what they were in this part of the world [i.e. England or thereabouts] in 1942 actually.... I mean I'm not a good enough mathematician or astronomer to work out whare they might have been 7,000 or 8,000 years ago, but as long as they correspond to some real configuration I thought that was good enough.
A different period again! Given the combination of the two comments, however, it is probably reasonable to assume Tolkien may have considered WWII to be the end of the Sixth Age. After all the end of previous Ages were marked by the defeat of evil:
- the First Age ending with the War of Wrath and defeat of Morgoth.
- the Second Age ending with the Last Alliance and the (first) defeat of Sauron.
- the Third Age ending with the defeat of Sauron.
So what could the Fourth and Fifth Ages be, if that speculation was correct? In a Biblical sense, the Exodus from Egypt and death of Christ could be candidates. In a historical sense, the founding of Rome, the founding of the Catholic Church, the East-West Schism, the First Crusade or the Reformation may all be candidates.
If Tolkien's statement of 6,000 years but that the Ages have quickened, I don't think it's unreasonable to assign the death of Christ and the founding of the Catholic Church to the end of the Fourth. That may make the Napoleonic Wars the end of the Fifth, given the threat of conquest from those, giving lengths of 4,000, 1,700 and 250 years to the Ages. Definitely quickening, but you could pick any two appropriate times to assign to the ends of the Ages and have it make equivalent sense.
There is an article published in the Tolkien Society's newsletter that attempts to calculate out the beginnings and ends of Ages without factoring in the potential quickening. It places the end of the Fourth to have just passed, in 2004.