Are there any chin implants that can give over 10mm projection?

Hello  - it's clear you have done your research.  The short answer is yes, we can get 10 mm projection or more and the vertical amount can be adjusted as necessary.  Chin fillers can help the deep groove but these are temporary.  I will often use a tissue transfer at the same time (some of your own tissue) to naturally and permanently fill that in.  Look at our videos and pictures to learn more.  I do a very large amount of jaw surgery adjusting things larger and smaller.  We also usually do this in a scar free fashion.

It takes a custom chin implant to provide over 10mm horizontal projection with some vertical length increase. The best method to decrease a deep labiomental fold is a dermal-fat graft not an injectable filler.

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  Non smiling, resting photos of your face from the front and side would help in the evaluation.   When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 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 (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.    There are numerous shapes and sizes of silastic chin implants, some of which are rather old shapes that do not yield the desired "natural" aesthetic results.  The Curvilinear shape is an example that is similar to the old "button" implants (had no wings or lateral tapering elements of the newer EAC design) that created a "pharaoh" shaped chin.  The EAC or extended anatomical chin implant style offers, in my experience and humble opinion, the most natural, aesthetic result when augmenting the chin.   Chin implants with projection of 10 mm or more would be quite thick in the front and the sides making stabilization and the aesthetic results questionable.  Similarly, it's quite rare that the lower face is vertically short, instead a weak chin results from a lack of forward projection in the chin.
Hope this helps.