As you can see from the patent’s drawing, it dates back from october 1987. I would be surprising that Northrop would not have proposed it. And as you said before yourself, it was rejected by the Air Force. Maybe Northrop was forced to use another design with 4 missiles because it was rejected, not sure about the details.

Also it appears that from looking at the drawing, those missiles are AMRAAMs with the large wings and fins. If you look carefully it seems that the distance between the missile is determined by the wingspan ( they would touch each other if they were closer ). With AIM-120Cs it could have been more compact vertically and narrower. 4 probably wouldn’t have fitted, 3 maybe.