Hmm. It sounds like the UniWS hack to fix the movies wetn bad, or the game's built-in movie player doesn't work correctly at 1920x1080 for some reason.
When you say the game works fine in the "native resolution," do you really mean it works fine when unpatched, or is the native resolution of your display not 1920x1080? If you do mean the movies are working fine for you when the game isn't patched, then what we can do is just not patch the movies so they will run at 1024x768.
-First use UniWS to unpatch the game and restore it to the original state. You don't need to remove the fixed HUD files or anything, just undo the UniWS part.
-Next open the patches.ini file that came with UniWS. You may want to open it with Wordpad as opposed to Notepad for easier editing. For whatever reason it was saved with non-standard newline characters so there are no line breaks when you open it in Notepad.
-Find the
[Star Wars: KOTOR (1024x768 interface)] section (which is what you should be using for the game to work with the edited files).
-Find these two entries under that section and either delete them, or put semi-colons (UniWS use them to designate comments) at the start of every line. Then save it.
Code:
;movies edit 1
p4modfile=swkotor.exe
p4undofile=swkotorc.undom1
p4sig=800200007515813DD8D17800E001
p4sigwild=00000000000000
p4xoffset=0
p4yoffset=12
p4occur=1
;movies edit 2
p5modfile=swkotor.exe
p5undofile=swkotorc.undom2
p5sig=80020000C7442410E001
p5sigwild=0000000000
p5xoffset=0
p5yoffset=8
p5occur=1
-Repatch with UniWS to your desired resolution.
As stated, these will make the movies run at 1024x768. So you may have a couple seconds of blankness as your display changes resolutions. Some HDTVs can be pretty slow to changes res.