I don't believe that either the Avant or the BeoSystem 1 can support 720p through the component cables. Only 1080i and 480p are supported. As I mentioned before, I actually find the s-video 480i connection to the Avant to look better than a component 480p signal. This is due to the Avant's video processing that is done on the 480i signal. Also, many older Avants had issues with the component input displaying "banding" and/or a magenta hue on the Avant's display. However, this problem does not affect the projector display.
Note that you CAN connect both the component and the s-video cables at the same time. If the signal is being output as 1080i through the component cables, the Avant will automatically accept the 480i signal coming through the s-video for it's internal display. It will still display the 1080i signal through the projector.
Also, because of the quirkiness of the Avant and the Beosystem 1, it might be necessary to use another tv connected to the device to make the initial setup of the device in order to establish the video signal that is being output. For example, it is impossible to setup a PlayStation 3 without first setting it up on another tv.