Congratulations, you've just been hired as the New Orleans Saints head coach. What are you going to do?

Serious answer:

A culture change has to be initiated. It doesn't have to be on the very first day but sometime early on, the new coach has to find their "Wayne Gandy's recliner" moment. The implicit message being "What we've been doing hasn't worked. At all. Adapt or move on."

One thing that might undermine this plan a bit is if any of the "gotta extend!" veterans are really locker-room problems. Not bad guys, say -- but maybe too-comfortable guys, or guys riding out the string, or guys no longer bothered by losing. If you can't waive 'em, you can demote them to second string. Without checking, I kind of think the gotta-extend crew are good dudes that will at least stay out of the way of true leadership ... but I'm not 100% on that.
This is the right answer. When you get hired as a coach you have to do some soul searching and build a culture and it has to be YOUR culture. I heard a great story from Steve Kerr about when he accepted the Warriors job and had a conversation with Pete Carrol about this. A coach who is TRYING to be someone they are not is bound to fail. Players need authenticity. You can do it a lot of different ways, but you have to set the standard. You have to come up with your vision, your culture statement, words etc. and then you have to live it every moment of every day. Assess buy-in and remove people who are NOT bought in. This first year -- dare I say the first moments -- are all about setting up the culture. Once that is done, then coaches can spend more time doing what THEY need to do to win and the culture takes care of a lot of the little things. When the players are holding each other accountable to the standard, that is when you know you have done it the right way. Coaching extends beyond the time you have them in front of you if the culture is something you can live. It extends to everything you do.