PS3 Audio Hardware – How to Use Headphones or Speakers with 3.5MM Jack on a TV Without Analog Output

I found a forum thread that suggests that you can do this: use the HDMI XBox cable to carry the picture through an HDMI-to-DVI converter, and then use the other XBox cable to carry sound (red and white wires).

However you may need to remove part of the connector base of one of the XBox cables so that both will fit in the XBox at the same time; apparently the 2 cables may not fit together at the same time.

Here is another thread discussing a similar idea. To research this, I Googled "hdmi to dvi adapter sound"

The delay is caused by two different factors. First, the television takes time to process the digital signal. Second, the game takes time to recognize the sound being played. The latter delay is unavoidable, but the former can be reduced by adjusting your television settings. Additionally, if the game knows exactly how bad the delay is, it can take that into account when determining whether or not you hit a note.

This article may have information you find useful. From the article:

Here are some simple steps to get you on your way:

• Use the in-game Display Lag Correction to help your note highway come down faster or slower. The default is set to 50ms is most cases!
• Make sure your console is set up to match your TV’s native resolution, whether it’s 480i to 1080p. In kind, make sure your TV is set up to match your console’s native resolution.
• If your TV has a “PC” or a “Game” setting, try activating that. Often, these settings may auto-correct some unwanted lag across all your games, and not just Rocksmith.
• If there are no PC/Game settings on your TV, access your TV’s options menu and fiddle with the settings here. Most prominently, image scaling and processing effects are going to be likely culprits. Deactivate them and you’ll probably see improvement.