Your log shows the problem surely doesn't have anything to do with GSX, because it says it cannot find an object called FSDT_Staircase_SQ, which is *SURELY* installed, since it's a standard object that comes with GSX.
The most likely reason is, you or another utility have altered the FSX.CFG file after it was modified by the GSX installer to include the Simobjectpaths to the GSX objects. This can happen, for example, if you restored the FSX.CFG to a previous state, one before the GSX installation.
Or, if your FSX.CFG was *corrupted*, the GSX installer hasn't touched it, to be sure it won't end up corrupting it even more.
Please post your FSX.CFG, usually located here:
%APPDATA%\Microsoft\FSX\FSX.CFG