"I would also imagine this would be an issue with games like Rock Band or Guitarsmith as it would feel more natural for me to hold the neck of the guitar in my right hand."
The majority of lefties play guitar in a right-hand fashion. They just fret like nobody's business, with lesser skill in picking. A smart lefty guitarist will use that to their advantage and write impressively fret-heavy work.
As to the original topic, the commonly used term in gaming for what you are looking for is a "southpaw" setting, in which the left and right sticks are swapped in function. Sometimes the top triggers are as well, but not as commonly. In your 360 settings under Profile > Game Defaults > Action > Movement you can change between Left Stick and Right Stick. Games should look to this and adjust automatically. "Should" is the key word there though. Across the board games pay attention to my Inverted Y setting with a 95% reliability, but I would not be surprised if that percentage is lower for the Movement setting.
In short, you are not looking for a list of games that support Southpaw. You just need to set your 360 up correctly.
Really though, the choice between left stick and right stick for movement and look is pretty arbitrary. They both require fine motor control. In the long run your better option really is to just learn the default so that you can play the greatest range of games without issue.