So it's not really that significant. In any case, what do either of these dates mean? I can tell you what they definitely don't mean - they don't mean the 22nd/23rd or 26th/27th days of the month Sextilis (not renamed August until 8 BC) in the consulship of Gnaeus Pompeius Magnus and Marcus Licinius Crassus (yes that Pompey and that Crassus). The Roman civic calendar was in a mess by the first century BC. A failure to apply intercalary months properly meant that the Roman civic year was about three months ahead of the solar year, something that Caesar had to rectify in 46 BC. So the last week of 'August' would have the conditions that would now be expected in May. This is certainly not when Caesar invaded Britain. He clearly states in De Bello Gallico 4.20, that the invasion was launched when there was little of the summer left (exigua parte aestatis reliqua). So 'August 22/23' actually means 'the equivalent of August 22/23 if the Roman civic calendar and the solar year were properly aligned' (i.e. on the Julian calendar). At which point the dates become, for me, rather meaningless.
I'm not even sure that the event can be dated to where August would have been. Apart from the reference to the summer, the only other dating evidence is that the landing took place four days before a full moon. I'm not sure why September is ruled out - in 1940 the Germans were certainly contemplating invasion in late September. Perhaps the astrological work and the studying of the tides demonstrates that the invasion cannot have been four days before a full moon, but eight or nine days (a textual correction proposed by R.G. Collingwood in 1937). But even this may be open to possible objections (as raised by others) that changes to the coastline over two thousand years have altered the currents. In any case, neither the 'traditional' date nor the new one seem to me to be terribly helpful.
At least these dates are less meaningless than the recent attempt to date the return of Odysseus (full article) to April 16, 1178 BC, on the basis of astronomical evidence from the text. Now, I'm happy with the notion that genuine astronomical phenomena are described in the Odyssey. It may be that the reference to the obliteration of the sun at Odyssey 20.356 is meant to be an eclipse. What I find far less plausible is the notion that Homer is able to insert consistent astronomical data into his imaginative account, that point to an eclipse five centuries before he wrote. Even the authors concede that their theory only works if one assumes that Zeus sending Hermes to Ogygia represents movement of the planet Mercury. Given that there are perfectly good dramatic reasons in the framework of the Odyssey for this trip (he's been sent by Zeus to tell Calypso to release Odysseus, and who else would Zeus send than the messenger god?), I don't see the need for an allegorical interpretation.
What both these items share, it seems to me, is a positivist outlook on the ancient world. Caesar invaded Britain on a particular day. Odysseus returned on a particular day. Since these are facts (an arguable proposition for Odysseus' return), then, the idea seems to be, it must be possible, with enough investigation, to discover those facts. With my own little post-modernist toolkit, I conclude that some facts simply aren't recoverable.
The title of this post, by the way, is a quotation from Monty Python's Life of Brian a series of captions that satirizes exactly this sort of attempt to advance precise dates.