Adjusting deadlatch so it doesn't fall into strike pocket
Best approach for adjusting the strike plate.


Size up where it seems the plate needs to go and how much offset it seems to need.
Remove the existing strike plate.
Fill the existing screw holes with a whittled pine plug that you glue with wood workers glue and pound into the hole.
Optional - If you are not into whittling a pine plug for the old screw holes you can try what many people do which is to dip tooth picks in the glue and shove as many as possible into the hole till it is not possible to insert any more.
Let the glue dry on the screw hole plugs.
Use a sharp chisel or very fine toothed hobby saw to cut off the excess screw hole plug material even with the jamb surface.
Mark and drill new pilot holes for the strike plate screws at the offsetted location. Remember that pilot holes for screws are smaller than the outside thread diameter of the screws but not smaller than the inner diameter of the screw thread.
Reinstall the strike plate using the screws into the new pilot holes. 
If you messed up you can always go back to step 1 and repeat.