Adding this grip-down motion to your arsenal isn’t a difficult change to make. As you can see in the photo above I’ve choked down about six inches and the only other changes I’ve made are to stand slightly closer to the ball and use a little more knee bend.
At my schools we preach the importance of the 20-foot putting stroke since 20 feet is the most common putt length in golf. So any student of mine facing a 15-foot putt on the course will preview some small adjustment to that 20-foot reference stroke during their pre-putt routine factoring in the other conditions of the putt that are computed as you read the green such as slope break grain wind etc.
You’ve got a built-in safety net already because playing the ball slightly back delofts the club as does abbreviating your backswing and follow-through. Check the photo below for what the punch looks like.