Personally I would not deal with meant for it. Solid silicone implants are what most plastic surgeon use. This should not be any different than doing a regular chin implant and I would guess most plastic surgeons should be comfortable doing this.
Another option is redoing the sliding...
A chin implant typically rests upon the lower aspect of the front part of jawbone and there are designs that can extend variably to the sides. These can be sutured to the periosteum or covering of the bone. Since they basically just sit above the bone in a precise pocket, they should not...
To provide a slight horizontal and vertical chin increase as well as keep the chin narrow a sliding genioplasty would create those exact changes. This will not alter your existing chin cleft.