I realize it's the only part of the installer not related to FSDT code
That's good you realized that, indicating it has nothing to do with GSX. At that stage, the installer is starting P3D itself, using the standard command-line mode that is the official way to install an add-on so, instead of meddling with XML and CFG files, we let the sim doing that, and it's the proper way suggested by LM.
So, it seems your issues is that, for some reason, P3D doesn't work for you when started from the command line, which can be caused by a variety of reasons, from activation issues to permission issues, to antivirus interference, but all related to the sim itself.