Fwiw I did recently, when I was getting near constant and unplayable No disconnection errors, sit down and step through the XBox Screen Calibration Guide. Long story short what made the screen fit FINALLY on my quite aging Samsung 47" Series7 750. Under Picture Options once I selected away from the 16:9 to a setting called "Just Scan". Hallelujah. Interestingly to type this little diddy. I went back to double check and its back to 16:9. And my game screen is still full view. Or Green Box per the Xbox Screen Calibration Guide.
On a smaller and probably similar in age 27" Spectre LCD TV w/ DVD in another room. All I had to do was change the input picture options from HDMI to HDMI PC. Got my Green Box/Full game screen there.
All the other settings are how darks are darks or how warm and bright this or that is. That's definitely more preferential. But these screen size format input setting finagling is definitely functionally key!
Hope this is helpful to some of yall.