This is not the answer I want, but I'm going to post it anyway because it may be helpful to some.
Here is the method to do it by editing the script for anyone else that wants to change options. Note that because I'm editing a default addon directly, it will need to be done every time a new version of Blender comes out, which is why I'd like to know if there is a way to do this with preferences.
Find the init.py file for the FBX import/export plugin:
<Blender install directory>\<version>\scripts\addons\io_scene_fbx__init__.py
In the ExportFBX class there are a number of properties, which all have name and default parameters. The name parameter is the text shown in the Blender UI, so you should be able to find the property you'd like to edit by searching for this string. Change the default parameter to that of your choosing. For example, to answer my question, I would change the default parameter of the property with name "Selected Objects" to True, and that of "Apply Unit" to False.