Hi, I have performed many chin augmentations, using chin implants, for over 30 years. Non smiling photos of your lower face from the front and side would help in the evaluation. A weak chin creates an imbalance making the nose appear larger, the mid face top heavy and the lower face look short that de-emphasizes the lips and allows early formation of a double chin. Chin augmentation using a chin implant will add projection to the chin creating harmony and balance to the lower face. I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty. I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone. It would be unusual (not impossible) that your chin has ideal forward projection (from what you have described) but if the photos reveal that it doesn't, a chin implant is far less invasive than a sliding genioplasty.
Hope this helps.
There is no standard style of chin implant that can make these specific dimensional changes. Such an implant design would have to be custom made off of a 3D CT scan of the patient. This is particularly relevant when you have such specific 3D chin changes in mind.
A full set of facial photographs are required to make a determination about being a candidate for a chin implant, due to the fact that the chin and the implants are both 3-dimensional structures. Chin implants are composed of Silastic, and can be custom carved when necessary. The primary goal for most chin implants is to give forward projection and some lateral width. The Mittleman pre-jowl implant can give 1-2 mm of forward projection and 4-5 mm of side projection on each side. Unfortunately, it will not give vertical height. For more information, diagrams of the implants themselves, and many examples, please see the link and the video below