Why do you think being from Anshei K’neses Hagedola means that he was around by the first Bayis.
As to Chazal being interested in dates, it is one thing to say that where they left it out, but quiet another to dismiss whole Sugyos discussing it in detail.
Keep in mind that clues can only hint, they aren’t hard fact. Chazal give us dates straight out. We can try to reconcile what we find, but it’s actually silly to dismiss the words of Chazal because of clues and pointers.