I finally found out how to get 4K textures to show up properly in AvP99/GE/Classic 2000.
These shots are taken in the multiplayer map Hive, an old one from the game's 1999 release. The first two are 4096x4096, the third image shows a 8192x2048 texture on the wall, the last one is a detail of that wall. All images are taken from in-game. The blood textures are taken from a 4K Blood mod for L4D2. Obviously, right-click and open in a new tab to see more detail.
It's kind of cool because the original game uses mostly 128x128 textures; even the good looking Redux mod by Mad Max RW used primarily 1024x1024 textures. The problem with these textures is the game can be finnicky with them. I'm not planning on retexturing any levels at this time because the degree of detail that I would require for the levels would be astronomical, since I would obviously make each polygon unique. But I wanted to share the fact that it's possible and some screens showing what it looks like.