Fuzz on LCDs filled with spaces?

Hi, I'm working on a multi-LCD project and am seeing some texture bleeding on what appear to be the glyph quads as well as the edge of the LCD, from one side to the other (see near the yellow highlight, right side).

Is it possible that having nearest-neighbor as an option for both glyph and overall LCD texture filtering would help this? Or is that too far from the aesthetic of the game? If the engine has a setting for it, I suspect setting the LCD...

Fuzz on LCDs filled with spaces?