This is only a problem with cheaper HDTVs. They aren't built to handle composite signals anymore. Higher end ones handle it better, but it still looks bad.
My Samsung doesn't do this. Composite looks HORRIBLE on my TV, but it definitely doesn't lag. HDTV's in general are just bad at interpreting the composite video input, and there won't really ever be fix for it unfortunately since it's considered "legacy" support. Your best bet is to use an old tube or CRT TV, since composite signals generally look best on one. If you're set on using the HDTV, you'll need to RGB mod your consoles, find an upscaler, and then plug in through the VGA port (which is what I'm doing with my projector). I believe S-Video should also mitigate some of that lag, but I can't confirm this.
You can easiy fix the problem with the Wii, use the component cables and set it to 480p. That way you're using a near HD signal (technically it's EDTV), and the TV can interpret it natively. There will be absolutely no lag and it will look a ton better.