This is a common procedure for us. We go through the inside of the mouth and can contour the bone and soft tissue for a better look.
Jaw surgery on the palate can be done, but it will not reduce the jaw.
Yes, we can make a chin implant of any size. It is easy to contour an implant the way you may wish. We do a lot of jaw and chin surgery. It should be fine to adjust with an implant over a prior genioplasty.
Either a sliding genioplasty or a chin implant will improve your facial balance. The lack of chin projection gives the appearance of a short lower face. By giving the chin more projection, the lower facial balance is improved.