I guess the video games probably aren’t canon, but I think it was The Force Unleashed that “revealed” that Vader intentionally planted the seeds of the Rebellion to create an opportunity to overthrow Palpatine, which makes all the times he or his troopers “fail” to stop the heroes make more sense.
OP already accounted for social situations where you would expect to meet people, though, and his parents seem to think that he should be approaching people in other situations—like in a store, or on the street. I’d be very cautious about that.