For the older games, you can try connecting the audio separately from the television using external speakers since the HDTV causes the audio to lag by upscaling the picture so it can display properly. You may want external speakers anyway since most DDR games support Pro Logic II. The three most recent Japanese versions (Supernova, Supernova 2 and X) and the American version of Dance Dance Revolution X support progressive scan by holding triangle and X as you boot the game. You will need to connect the PS2 to the television via component cable. Enabling progressive scan means the game will have already upscaled the image so that the HDTV doesn't have to.
This is DDR. Don't hate the game; hate the player.