If I'm Woody, day after the second Fish game I fire Idzik. No matter what the Jets do the last 6 games.
That's the only firing I do. I go out and hire a football orientated GM. One that has a strong background in Scouting, and personnel. Give him total power over the football operations.
Once the GM is hired, let him do what he wants with every employee of the team. Why interfere with his selection of coach. It didn't work out so well with Idzik. If he wants Rex back, so be it.
I think it is a very long shot Rex is retained, but you never know. I do think Rex will be a HC in the league within a year or so