The pics were not visible until I registered as a user. Very helpful. That door lock was driving me crazy for the longest time.
I took a slightly different approach after drilling out the rivet. At Home Depot I bought a Binding Post with Screw, 3/16" x 1/4" and used that instead of a machine screw. It's basically a smooth shaft with a cap on one end and the other piece is the screw that goes into the shaft. Both sides have a pretty broad and flat cap, so no washers were necessary. I used blue thread lock to lock it in place. Note: the plastic actuator that the rivet had previously gone through was 3/16 already. I had to widen the hole in the metal housing using a 3/16 drill bit to get the binding post to fit through.
Thanks again for the great fix!