I eventually located a licensed version (2.51) of Pathfinder Office in another department which a) did not require a hardware key to use, and b) installed and ran on a Windows XP virtual machine.
In order successfully export to shapefile I needed to go into the advanced options screen under export and check all options under the [Attributes] tab, and also check the boxes for "create point features from Notes, Velocity, and Sensor Records". There is a pdf document called "Exporting into an ESRI Shape File from GPS Pathfinder Office" from California Surveying and Drafting Supply (link points to Google docs quick view, I don't know if that works for everyone.) which covers the process. It's for version 5 but most of the options were pretty much the same.
Before setting the advanced options the Export utility would say things like "1587 positions read. There are no features to export".
Don't forget to set the coordinate system manually for the shapefiles afterwards, as Pathfinder Office doesn't create a .prj file. Unless you change something it will be
We had two licensed copies of Pathfinder Office, v2.11 and v2.21, including hardware dongle, but neither of them would install or run properly on our current hardware or virtual machines.
Moral of the story: future proof your data. Storing a plain text copy only takes an extra minute or two and can save a lot of headache and money next decade.