I'd second Grumman, but I'd also suggest Martin and Douglas. True, neither had recent fighter experience, but both had competent design staffs. I'd also consider Bellanca: Giuseppe Bellanca was brilliant, and produced some very efficient, robust aircraft, and Northrop, although his one design to see production during WW2 was hardly amazing. Just don't let him build a flying wing.
There were a lot of large aircraft manufacturers, but quite a few of them had no recent fighter design experience (of course, neither did North American!). I'd stay as far away from Hughes as possible; Howard would rhymes-with-muck up anything due to his ego and other personality flaws.