Cutting the logo down the line you have and placing a light barrier (like thin black paper) then gluing back together would work better i'd think. The logo is side lit not lit from underneath, correct me if im wrong.
It'd probably work better if the mod also put white paper behind that hole in the display PCB. Otherwise a certain percentage of coloured light will bounce off the transparent plastic, off the back of the LCD, and then through the other side, lighting up the far end of the opposite letter in the wrong colour. To keep all light from the wrong side, the two barrier papers would need to connect, otherwise some light will bounce between the gap.