Move chin down to fix mental crease? (Photos)

Your chin does have strong forward projection, and this is evident by the relationship to the lower lip and the depth of your Labiomental sulcus.
Converting the anterior projection to inferior projection with a sliding genioplasty would give a slightly better balanced profile image.
To make a quality assessment we need quality pictures.
For profile pictures have someone else take the picture or use the timer on your camera.
Avoid taking pictures with you turning your neck.
Try to take the profile picture at straight angles. You also need to consider your jawline and make sure that that is not deviated too much by having the chin turned downwards.
Overall, it seems like oral surgeons do more of these procedures than plastic surgeons, but training is not as important as actual hands-on experience.
Consider consulting with both oral surgeons and plastic surgeons in your community to see what they have to say.
Bring a set of proper facial pictures to use as a reference during the consultation.
During each consultation, ask each provider to open up their portfolio and show you their entire collection of before, and after pictures of previous patients who had similar facial characteristics to your own period
A sufficiently experience provider should have taken care of previous patient who had similar mandibular characteristics.
Best,
Mats Hagstrom MD