I am now getting around to GSX, the installer gsx_fsx_setup appears to want to install into FSX
It's not very clear from your post if you just downloaded the GSX setup now, or you are trying to install into P3D using an older GSX installer which was made before P3D4 was supported.
Of course, the latter wouldn't work and it's entirely normal an old installer would try to install into FSX, since it's still installed.
The current installer, of course, fully support P3D4 so, it will present you with a choice, which by default will install into both FSX and P3D4 (or any other supported sim you might still have installed), then you can check/uncheck the options, if for some reason you don't want to install in one of the sim.
And please note, the current installer will NOT install "INTO" the sim anymore.
It will install in its own shared folder ( C:\Program Files\Addon Manager, by default), with the obvious advantage that, if you want to use it in multiple sim, it will not waste any hard drive space with multiple copies of it, like it used to be before.
So, just be sure you download the CURRENT GSX full installer, not something you downloaded a while ago, which might not be a P3D4-compatible version.
And yes, the installer is still called gsx_fsx_setup.exe, but supports FSX, P3D1, 2, 3 and 4