Over projecting chins can be reduced with a genioplasty. An incision is placed on the inside of the mouth and the end of the bone is cut and pushed back. It is secured with plates or wires. It is not possible to push it back an inch. It is difficult to tell by looking at the pictures, but you may be able to make the lips a little fuller which will make the chin softer.
Your chin can be v vertically shortened by an intraoral vertical reduction genioplasty. But an inch (25mms) is not a realistic amount nor the amount of reduction you actually need. More likely it is in the 7 to 10mm rrange. It is also importahjt to be aware of what happens to the jawline behind the chin when it becomes vertically shorter as this will disrupt the line of the mandibular plane. This would have to be addressed at the same time.