Have you ever paid attention to how critical your left elbow action is to enable good wedge play? In this tip from Rob Stanger he showcases how the soft left elbow is a component that can really help you with consistent solid strikes on the ball.
Many mid handicappers try to "push" their hands down the line and chase after the ball. You can see that this is NOT what Rob does. It is the opposite. The soft left elbow allows Rob to pull the handle of the club and the hands to come up and inside as the club head strikes the ball.
Try this on your next wedge practice session and you will find that the feeling will really help you control your club face action through impact.