My deep mentolabial fold and chin shape worry me. Possible solutions? (photo)

Because moving the whole lower forward causes the teeth behind the fold to come forward,  the labiomental fold is softened. But this requires orthognathic surgery which may or may be indicated based one your current bite relationship. Short of that procedure any chin augmentation method must factor in how to directly soften the depth of the fold at the same time.

A chin implant can be placed to soften your labiomental groove and improve you chin projection, akin to the maneuver that you described when you push your jaw forward.  Hope this helps.