I can give you some conceptual info.
1: The rule of ' 1/3rds' was first put forth by Leonardo and Dürer (master artists) as a guideline for drawing a normal face. It was not meant to be the
sin qua non for ideal beauty or handsomeness.
2: As to the lower '1/3rd' subnasa to base of chin, the FARKAS ratios for Anthropometry can be used which are norms based on scientific measurements of different types of people; races, ethic groups, male/female, age, etc. A shorter lower '1/3rd' is within the norm of some groups, eg. Eastern Europeans.
3: The chin is measured (relatively) in it's own right INDEPENDENT of jaw advancement. For example, if you drop a straight vertical line from your lower lip and if the chin is very close to it or actually ON that line, there is NO (aesthetic) NEED for independent chin advancement. A vertical line on your TILTED picture is one parallel to the hang of the curtain in the background. With reference to that, your chin is not recessed. (ref=
https://imgur.com/BGfVmAz)
4: When you jut out the jaw, you are moving BOTH the jaw and the chin outward along somewhat of a downward diagonal. Yes, your chin will cast both more prominent and longer (because it's moving outward and down along a downward diagonal). But the act of doing so is NOT an independent diagnostic for isolated chin advancement. (Because it's movement is DEPENDENT on jutting out your JAW. You are not moving your chin independent of also moving the jaw)
5: The basic visual diagnostic for relative lower jaw recession (independent of the chin!) is to drop a vertical (again, a line parallel to the hang of the curtain in your tilted profile photo) from the upper lip. If the lower lip is BEHIND it (which yours is), it's a basic indicator that the lower jaw is relatively behind the upper jaw. Another way to 'see' this is to look at the lips in frontal. When your upper lip looks BIGGER than your lower when your jaw is NOT jutted out but when your lower lip looks more 'equal' to your upper lip when your jaw IS jutted out, it's because jutting the jaw out brings the lower lip MORE into the FOREGROUND. So, that should at least give you some clue that isolated chin displacement is NOT going to reproduce the visage of jutting out your jaw.
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The above is just a conceptual method as how to SEE things correctly as to not fool yourself into thinking you're 'seeing' an isolated genio by how you are posturing your jaw. Of course, that does not preclude a surgeon from accommodating a request for a longer and more advanced chin. I would suggest you go into the consult with the basic conceptual info I've mentioned above, jut out your jaw for him/her and simply ask IF what he/she sees on your CEPHS allows for a displacement that would come close to it. That would be the very OBVIOUS question for you to ask.