I suggest slicing your images into regions based on their overall color content, and the applying the best compression settings to the individual slices. Without slicing the image, one setting applies to the whole image, and that it may not be optimal for the color range of the image.
For example, your sample image can be sliced into 3 sections - the shaded text overlay and the two borders. The overlay slice can be compressed with gif, and the borders can be compressed with jpeg, at whatever quality settings look the best.