Gap between door and frame is too large at latch location
This likely has nothing to do with the casing installation, but with the set of the door frame (jamb). You're right that you should shim the strike area further out from the framing. It's also possible that atypically long screws were used for the strike plate and over-tightened, pulling the jamb in.

* UPDATE* 
From the photos in your other question I now realize that this is an exterior door. It's very likely the case that long security screws in the strike were tightened too much. (Though a good carpenter would've shimmed at that location when the door was installed, preventing the problem.)

Remove just the strike plate and use a small pry bar to check whether the frame will move easily. You'll need to overcome the force of the casing nails and any nails through the jamb and into the framing.

Another option is to run a construction or drywall screw into the jamb in the strike plate mortise and use it to pull the jamb. Don't get too rough or you could split the casing if there are nails right there.

If you can move the jamb, use any available means to shim it out a bit--a wad of paper, a screw through the jamb and behind the strike plate, or whatever. It doesn't need to be complicated or overly robust. 

Once the jamb is in the right position, install a countersunk, piloted, full-thread screw behind the strike plate to lock the jamb in place. Re-install the strike plate.