Okay, I got it working. First off, I wanted to expound on my unique file setup. All my vps are in /mnt/windows/Games/Freespace2 whereas fs2_open_r is in /usr/local/games/fs2_open. In that same folder, there is a script wich does:
cd /mnt/windows/Games/Freespace2
/usr/local/games/fs2_open/fs2_open_r -switches_galore
Now, I already had warpball01.tga in the VP folder, as that is where it is run from under windows, but under Linux it just wouldn't work. I tried putting warpball01.tga in /usr/local/games/fs2_open but that didn't work either. Then I remembered that fs2_open stores some data in ~/.fs2_open. So, I tried putting warpball01.tga there, and voila! It worked! So, my warps are all cool now and I am happy. Now I'm wondering, is there any way to use cutscenes under Linux? I've got the .avi files and I've tried them in all the locations, but they don't play.