Would a genioplasty help me achieve more projection and vertical lengthening in the lower third? (photos)

Based on your photos you would benefit from increased horizontal projection. This can be accomplished with a sliding genioplasty or chin implant. Corrective jaw surgery is unnecessary if you can eat a normal diet and are only interested in a cosmetic improvement. The sliding genioplasty is a better procedure for vertical lengthening than an implant. Both procedures are performed in my office under intravenous anesthesia and the surgery does not change your bite. Most patients return to work within 3-5 days.

For purely cosmetic purposes, you could undergo a chin implant procedure under local anesthesia in the office setting, which takes about 30 minutes. Placement of a solid silicone chin implant is placed through a small incision underneath the chin, and can accomplish augmenting your chin forward, with a small amount of vertical height, and a small amount of width as well. It's also quite easy to remove these implants if you don't like the improvement

Your chin or mentis region of your mandible does not project well, so you’re definitely a good candidate for a sliding genial plasty.
That by itself will not advance your mandible where the deficit is more significant which is behind your molars in the body of the mandible.
In other words, a sliding genioplasty will only give you improvements in the chin, but will not advance the entire jaw , which is really what you need.
Nobody wants to have jaw surgery.
I get that.
No one has to have cosmetic surgery.
A limited procedure is going to give you limited improvements.
I recommend having multiple in person consultations with other oral surgeons in your community to get a better understanding and get some consistency among recommendations.
I do not recommend patients rely on virtual consultations and instead always rely on in person consultations.
During each consultation, bring pictures of your face like the ones you’ve included here.
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.
Highly experienced surgeons should have access to hundreds or preferably thousands of before and after pictures to choose from.
By seeing quality collection of appropriate before, and after pictures, you should have a clear understanding of what your results are likely to look like.
There should be no question regarding what each procedure can and cannot accomplish.
If the provider is unable to accomplish this level of communication then you need to continue having more consultations.
A sliding genioplasty shouldn’t burn any bridges for having more extensive surgery later. There’s also something to be said about doing the correct procedure the first time.
It is however, insufficient to really fix the problem so it depends what you’re trying to achieve and what you’re willing to go through.
When in doubt, slow down and schedule more consultations.
Best,
Mats Hagstrom MD