I posted this before on another forum, but it could be of value for someone.
I just finished installing a new Schlage Lock (stainless steel, commercial applications) and it worked out real good. I didn't even have to adjust the thickness of the lock. And it was adjustable from 2 3/8 to 2 3/4 (backset) from the edge of the door. I used the 2 3/4 and cleared the screen door frame on the inside.
I will cut an access opening in the screen, so I can lock it from the inside as well.
This is a very secure lock.
Caution: Airstream does not recommend using a regular dead bolt, due to weakening of the door frame.