Greetings, ElMarfacho and Thercio (and anyone else reading this post)!
I'm not going to call myself an expert by any means, but I just got this mod working on my 1600x900 display after running into the same problems you're talking about. I think I know what you need to do to get this mod to work.
I'd already had UniWS's GOG file working correctly, but that's not the only patch you need for the mod to work correctly. The ReadMe file assumes you know you need to patch the swkotor.exe file twice, and I'm just going to chalk it up to my own ignorance.
Here's what I did:
First Patch Job - Widescreen fix with UniWS (if you patched this using 1024x768 interface to your new display size, you can skim past this part):
Copy your game's original swkotor.exe file and save it somewhere as a backup.
Additionally, if you're a Steam user, go find a usable "cracked" swkotor.exe file that you can adjust, since Steam's file won't work. Just Google/Bing/DuckDuckGo/etc. "Kotor no-CD" and that's how I found mine. Once you have a usable swkotor.exe file, save it somewhere else as a backup.
In UniWS, patch your swkotor.exe file using the 1024x768 interface instead of the 800x600 interface. I know the file was patched because I got feedback from UniWS saying the patch was successful.
In case you haven't, go ahead and run this swkotor.exe and make sure the game is running at the new resolution. Other posters in this forum have indicated you need the new resolution implemented in the game before installing this mod.
Second Patch Job - Mod Prep (if your mouse is off and HUD boxes appear on the menu screens, this is probably what you missed):
Copy the patched swkotor.exe file to the Hi-Res-Menu Mod folder
Referencing the ReadMe file, we are now at "Step 1: Modified Executable swkotor.exe"
Double-click hires_patcher.bat and enter the information. (Note: I did NOT have to Run as Administrator, but keep that in mind if you need to troubleshoot.) For my 1600x900 display, which is in the 16:9 range that ndix UR recommends adjusting the letterbox for, I entered 1600, 900, yes, swkotor.exe [well, I just hit Enter for this last one since my .exe file sitting in there is called "swkotor.exe"]
After the patcher program finished, I verified that a swkotor.bak.exe file was created. That's the easiest way to see that your second patch job was successful.
Installing the Patched .exe and Mod:
Copy the new swkotor.exe file from the Second Patch Job (not the backup!) into your game folder
Copy all the appropriate .gui files into the game's Override folder (for me, that's the 1600x900 gui files)
Testing the Mod:
The main menu screen will always work
Start a new game and you'll know it's working if your loading screen is properly sized and not running off the screen like it would if you're using a single-patched instead of a double-patched swkotor.exe file.
Go to any other menu and see if your mouse lines up with the buttons
Until ndix UR or an impatient modder makes a patch for the map, the map will be small. I imagine you can remove that specific gui file from the Override (map.gui) and get the old map back, though I don't know if your mouse will line up with the map's buttons correctly.
You might notice extra border lines at the top and bottom during dialogue. I imagine this is ndix UR's way of ensuring all the dialogue text stays on-screen.
You might notice some bright blue borders that no longer match the image/descriptions. I definitely caught this on the Items menu, but it's not a deal-breaker for having a widescreen menu with more items-per-page.
May the Force be with you!
Since the Steam swkotor.exe file doesn't work, you have to go online and look for a "Kotor non-CD" file. I was able to find one just fine, but I think it's illegal for me to upload it here since it's not really my file.
Not the expert here, but I imagine a manually hex-edited .exe would be fine. You'll still need to run it through the other patcher that you download with the mod, or your mouse won't line up with your buttons and you'll see HUD buttons in the submenus (as several in this thread have mentioned).