All right, so currently my PS3 is connected to my TV via the HDMI and those cruddy composite cables -- the yellow, white, and red. Why both? Because my TV has channels dedicated to both. When I run a PS2 game on the HDMI channel, yeah, it looks bad. So what do I do? Go to my Display Settings and swap the PS3 back onto the 480i channel -- the channel most PS2 games were probably meant to be seen in. I think that's the problem -- PS2 games didn't plan on getting their resolutions increased so drastically. Anyway... so I swap it back to 480i and re-load the PS2 game and guess what? The text is gorgeous and the graphics look fine. I think. They don't look perfect, but it's a lot better than the HDMI shows.
You guys can go ahead and test this if your TV is prepared for the journey of multiple wires. Or computer monitor, which I know a lot of you swear by (and rightly so, it seems)! Let us know if this works for you. In all seriousness, though, it doesn't bother me that much. If I can still enjoy the gameplay, I don't mind having a jaggy sword, or funny-looking handrails. Perhaps Sony will strive to fix this in the future, but for now, keep your PS2 hooked up if it gets too unbearable.
[update: As I continue to screw around with different games, if you crack out any 2D-centric titles (Atelier Iris 2 in my case), the graphics actually look better with HDMI. The backgrounds have a few splotchy points, but the sprites are much, much sharper.]