Most PC monitors do a wretched job upscaling lower resolutions. I have a newer Samsung and it's just terrible for gaming at resolutions below 1080p (and even then, it's not great).
You still have your CRT? I know the resolution isn't on par with the LCD, but I still think most games would look much better on that CRT. While there is less visible detail, you can see how much smoother the games look.
The LCD I use was actually something I had to settle for. I was looking for a large monitor for the back room that could double as a display for 360 and PS3 (for friends to use when networking). I initially went searching for a large CRT and I found some for dirt cheap, but I could not locate any of the 16:10 CRTs and the ones I DID find all have issues at this point due to their age. If you could find one of those 24" Sony widescreen CRT monitors, that would be optimal (they are beastly, though).
I believe you are in a unique position in that you still remember how damn good CRTs look. Most people seem to have forgotten and have simply become accustomed to LCDs for PC gaming. A good CRT still wipes the floor with every LCD in most areas when it comes to PC gaming.
try playing games in windowed mode
That's not a great solution, though. I mean, who really wants to play a game in windowed mode? That just kills the experience, if you ask me.