You may have better luck if you limit your calibration efforts to the center of the screen.
The display "gamma" (for lack of a better term) of LCDs varies with angle of view. Colors along the edge of the screen appear different from the "same" colors in the center of the screen. Although newer monitors with wider viewing angles exhibit the effect to a lesser extent, it is still present. The uneven color is caused by the monitor's use of polarized light.
The larger the monitor, the greater the variance because of the increased angle between your eyes and the corners of the screen. If you sit farther away from the screen, that angle will be reduced, and the color differences should be less distracting.
The device in question is a TV. I suspect TVs have lower resolution and color standards than computer monitors because they are meant to be viewed from a much farther distance.
LED refers to the source of the back light. It still uses the same basic LCD technology.