I don’t agree trying to get the stairs open right after take off means he was delayed in jumping. That’s a jump in logic.
He has only one way out, securing that pathway is the top priority after take off. That doesn’t mean he wanted to jump instantly. It means he wanted to secure his escape route for when he was ready. Thinking he was ready and wanting to jump five minutes after take off is an assumption.
I’ve also thought more about your theory on Cooper wanting to go to Mexico. I think he read or was told the max range which is about Mexico City. Cooper is not a 727 expert. He didn’t adjust for fuel consumption flying dirty, he was way off. But…he knew the plane could make it to the middle of Mexico flying normal. If his goal was truly to jump across the border he can just tell them to forget flying in the 15 degree, flaps down configuration and head to Mexico. Basically, there is a clear way to achieve that goal given his knowledge and capacities. He chose not to insist on Mexico. He chose flying dirty over distance. He knew he was going to jump way before Reno. That was his plan.