Even the geography will be different. No Las Vegas = Hammer Falls without the Thor license. They could have Magneto be one warlord and Dr. Doom the other, if they want to revisit the Incredible Crash Dummies Doom they created. It's going to be so many different substitutions and compromises that I wish that they would pick another story. There are so many good Wolverine stories out there, that they don't have to shoehorn in Old Man Logan. Heck, make it a movie where Daken is first introduced. Or X-23.
Tie it into the Weapon X story where they went underground and rather than control Wolverine, tried to clone him. It took 23 attempts, but X-23 was finally created. X-23 is sent by the new Weapon X to take Wolverine out. They fight, yada, yada, yada and X-23 comes to realize how she's been manipulatd by Weapon X and Wolverine just wants to be left alone and retire in peace. Final scene is a girl named Laura Kinney being dropped off at the Xavier Institute and Logan saying "There are good people here. People like us. Mutants. They helped me once when I had nowhere else to turn and evolved me from an animal into a hero. They can do the same thing for you."
Cue X-23/Laura Kinney as the "new" Wolverine in the X-Men flicks so you don't have to re-cast Logan.