Can you post screenshots of your C:\GOG Games\FreeSpace 2 folder, your Basic tab, and your Advanced tab?
There are a few things to check here: your build (19-RC2 without AVX), the folder itself, your settings (1024x768 to be sure), and your command line (presets off).
If all else fails, you can still play ST:R with retail, but that involves moving .vp files out of their mod folders which is risky if you don't know what you're doing.
What happens if you play FS2 through GOG without any FSO or mod stuff? Do you see the ship graphics then?