In answer to your questions, if it breaches your stop by a few pips, then tough. The stop has been chosen to accommodate noise, though, so it is less probably an occurence. Why not a better price? Because you're trying to make the most of a dead trade. It isn't a guarantee that the AH won't fail, of course. You also want assurance (confirmation?) that the movement is now back in the direction of the trend.
The market reveals who we really are...