Dropping your jaw and sucking in your cheeks won't mimic outcomes of surgery. So, doing that in front of the mirror can't be relied on as to how you will look in the mirror subsequent to maxfax surgery. Sucking in the cheeks sucks in the buccal fat pad which, in turn, accentuates the cheek bones. Maxfax surgery doesn't do that. Also, doing that in front of mirror moves ONLY the lower jaw and although you are not looking at the LARGE SPACE between your upper and lower teeth while doing that, that's what is going on inside your mouth while doing that. So, I would disband with any expectation you might have of surgery kicking up that particular desired result.
When the bite is 'made right' by prior ortho, it's usually UNDONE in preparation for surgery. This is called 'decompensation' which can resolve to TIME in braces to prepare for what ever movements are to be made in surgery for the jaws to line up in more favorable position and also for the bite to mesh.
Elongating the lower '1/3rd' of the face can involve a graft to the entire maxilla. The NET rotation of the graft can be either net CCW or net CW or even NET rotation of 0 if the graft is uniform vertical length to the entire maxilla. So, a graft to the entire maxilla can elongate the lower 1/3rd. Further adjustments to elongate could/would involve a type of genioplasty that goes 'down and out' (diagonally downward). Since a GAP is left via that type of genio, a bone buttress (another graft) is sandwiched inbetween the cut segment of the chin and the part of chin the segment was cut from. Technically speaking that type of elongation is actually done to the 'middle' 1/3d of the face but the increase in length is seen to the lower 1/3rd.
The best candidates for an elongation graft to the entire maxilla are people who can be described as having 'short face' and/or 'short chin' and ALSO have LACK OF upper TOOTH SHOW. Basically, if they have a VERTICALLY SHORT maxilla and that is found as the main reason they have short face, LACK OF UPPER TOOTH SHOW also exists. For example, IF someone had plenty of upper front tooth show, vertical elongation would kick up a gummy smile and excess tooth show. Hence lack of upper tooth show needs to be an indicator. This concept also applies to an isolated graft to the anterior maxilla (CW-r), lack of upper tooth show would need to be part of the problem set.
'Short face' is basically a vertically short maxilla and you could get some idea if you had that by SMILING in the mirror and seeing very little tooth show. Some people, have a vertically short mandible and elect to elongate that way by either jaw implants with a 'drop down' or 'chin wings' with a bone graft to 'drop down' the lower border of the mandible including the chin.