I finally got around to removing and re-installing the game and made it a full 15-20 minutes standing around in crowded Limsa Nominsa before it crashed... Got my hopes up for a bit and then - crash.
I hope Square Enix figures out what the problem is, but based on our help desk experiences it seems unlikely that they will even admit something is wrong with their code.
Windows tells me that there is an unhandled exception and memory is being written to invalid locations (when I click on debug after the error). As a programmer, I know that exceptions are not usually that hard to catch.