I hate to point to the same source again, but the Richard Carrier article specifically addresses the eclipse claims. He cites his sources in his refutations, so there's no need to simply take his word for it. Here's another link to it: http://www.harrington-sites.com/Carrier.htm
But it really is laborious to go through all the claims of these various apologists to find where they make speculative leaps, cherry-pick references, contradict well-established historical data, etc. Let's look at the bigger picture here: We have a wealth of converging data from various sources, some direct, some indirect, some circumstantial, which all point to things like Herod dying by 4 B.C., Quirinius being governor of Syria in 6 AD, and a local census for tax purposes being carried out in Judea at that time.
The apologist, however, wants to place Luke's events around 4 (or 3 or 2) B.C., because their purpose is to make Luke agree with Matthew, (and they CAN'T place Matthew's events in 6 A.D.), So they say, well, maybe Herod lived until 1 B.C., AND Quirinius had an earlier term in Judea, AND a census was carried out in 3 BC for a loyalty oath, etc.
The problem is that there is NO EVIDENCE in the record for ANY of these events. So apologists go digging through the sources to mine tiny bits of information that could be consistent with their ad hoc theories, like somebody in the 2nd century calling Quirinius a "procurator," or Josephus' alleged confusion over ONE date for ONE of Herod's successors. The ancient sources are far from perfect - one can always find discrepancies, apparent errors, points of confusion, stray bits of information that don't agree with others, etc. But these don't outweigh the much greater and more consistent body of evidence that support the mainstream historical accounts, and they don't begin to establish that the events imagined by apologists actually took place.
It's not possible to definitively disprove every speculative theory that apologists can come up with. But shouldn't the burden be on them to prove them? Flew, I would ask you: Can you find any reputable historians or even mainstream bible scholars WHO ARE NOT CONSERVATIVE APOLOGISTS who support these claims? If the apologists have compelling evidence, why aren't these claims accepted by historians?