I managed to get 1920x1080 working, using Flawless Widescreen. But to do it, I had to set swkotor.exe to run under Windows XP SP 2 compatibility mode. I also had to download the 32-bit version of Flawless Widescreen (I chose the porable version), and I had to set it to Windows XP SP 2 compatibility and to run as administrator.
Then it worked. I assume running the game twice was necessary, but I had run the 64 bit install version and tried several times, so I'm not 10% sure on this point.
I'm running Windows 8.1 64 bit.