So, I found a pretty cool forum post on UT99.org that walks you through downloading an updated texture pack and also some configuration tweaks for the game. I tested this out and I can now run the game at higher resolutions (1920×1080 for me) and the game seems to look, sound, and run much better.
If there's one thing we love, it's incredibly customizable games! Not only do they allow for some great mods, but they usually survive the tide of ever-changing technology much better than games that are locked down. UT99 is definitely one of those. Anyone who can edit a file in Notepad can get it to run in HD even though it came out more than 10 years ago.
I use the texture pack on my own PC and it's definitely awesome, although for the LAN parties I use a separate copy with no mods, just to make sure it doesn't serve those huge textures to some of the older computers in the room.