Looking again I wonder if both jaws are somewhat retruded which might explain why we were misled. The relative relationship between jaws looks quite good. Also I notice how straight the C-spine is (cervical kyphosis). This can accentuate any double chin appearance.
Yes, the head posture is very 'backward' and it's making the chin look worse than it is
I think both jaws are a bit retruded, but the bite looks good. You could get bimax advancement with a bit of rotation, small advancement of the maxilla (~3mm) (+maybe a tiny bit of impaction?) and larger advancement of the mandible (~7mm) but I also think you would get a really decent result from a genio and under-chin lipo. I also carried a lot of fat under the chin - even as a 90lb 15 year old I had a bad double chin. I got lipo and the result was amazing so consider it, especially as you bite is decent. Depends how bad your functional issues are. You are lucky in that you wouldn't need braces for very long, and in your case the surgical path looks pretty straightforward.
I don't think a BSSO alone is a good move because I can't see how they will create a big enough overjet to move the jaw much without doing extractions. I have a much bigger skeletal overjet and I was told the most I could get through BSSO alone was a 6mm advancement. For you it would be about 3mm, 4mm at a max - you might as well do a genio.
As for lifting the cheeks, the options are
1) cheek (midface) lift with endotine
2) cheekbone augmentation with HA or implants
3) cheekbone augmentation with deeply placed, dense filler (e.g. radiesse, perfetha subskin)
4) Korean V-lift (results last about 2 years)
5) reduction of buccal fat and/or microliposuction around the lower face
Early sagging of the cheeks is common when there is less bony support