Your problem is caused by the fact the registry key for FSX:SE is the one used when both FSX and FSX:SE are installed together, but there's no FSX installed.
More precisely, the FSX registry key points to the FSX:SE installation, but in this case, you shouldn't have the FSX:SE registry key, because the FSX:SE registry key should be there ONLY if you have BOTH versions installer.
A correct registry for FSX:SE installed stand-alone is the *FSX* registry key pointing to the FSX:SE folder, and NO FSX:SE registry key or, more precisely, no "AppPath" sub-key in it, which I think it must have been wrongly added by some addon product.
Removing the AppPath key from the FSX:SE registry key located here:
HKEY_CURRENT_USER\Software\Microsoft\Microsoft Games\Flight Simulator - Steam Edition\10.0
should be enough to complete the installation. Pay attention to remove it from THIS key, not the FSX one!! ( Software\Microsoft\Microsoft Games\Flight Simulator\10.0 )