If you're within 50 yards of the flag, and you want your wedge shots to stick to the green like Velcro, stop being such a stiff! Let your body naturally turn toward the target on the downswing, just as you would on a normal shot. Your work is only halfway done at impact—a full finish is mandatory.
First, don't worry about a big turn. Simply hinge the club up with your wrists until your arms are roughly parallel with the ground. This provides plenty of energy to get the ball to the green. Next, rotate your body down and through the shot until your chest—followed by your head—faces the target. It's okay to keep your head down through impact, but don't lock it in place after contact. That can "freeze" the body, leading to overly active wrists that flip the clubhead past your hands.
When you're less than 50 yards from the green, simply hinge the clubhead up in your takeaway. This provides enough power to reach the green. No need to make a full swing.
Impact is just the halfway point of your swing. After contact, let your shoulders and chest turn naturally toward the target, followed by your head.