Here's the thing. Woody is not a football man. Never was, never will be. He should base his choice on which candidate has the most experience and success. You think Belichik was hired based on his interview? Results do not lie.
I do not believe Woody will harbor ulterior motives when he chooses a new GM. He will choose the candidate he believes will do the best job for the Jets.
However, that has no bearing on whether or not he will make a good choice.