IMHO the easiest and cheapest solution is to use a component to HDMI or component to DVI converter box. Hauppage HD PVR has a passthrough which doesn't lag. And if you use a decent converter box, there should be no lag or much quality loss.

You can connect the HDMI output of your xbox to an HDMI splitter. Then connect one output of the splitter to your monitor and another one to an HDMI to component converter.

The first ViewHD product has great reviews, and should work fine for you. But it is pricey and you will also need an HDMI splitter when using it.