With or without the cover has no effect on the airbox hitting the cable, because the lower left corner of the box is what hits the cable. I've tried fitting it in without the cover and I have the same problem. I measured mine from the center of the filter element to the left side of the box and it was the same as yours.
How far above the engine mount bolt does your air box sit? I wish I knew someone else around here with a grande, because it sounds like our bikes are set up the same way, but for some reason mine just doesn't fit right. I'm thinking of just cutting the box part off of the airbox, so all I have is the filter and the part of the box that houses that. I've got jets up to #60, so it's not a problem there.