This is my life

Really enjoying this discussion.
I think you can make a case for Sheppard having a 'false self', stemming from his messed-up childhood and/or adolescence. Depends when you want to imagine he lost his mother, who isn't mentioned in canon really. If he lost her early he's going to potentially have some quite dysfunctional defences and maybe have a veneer of coping when things are good, that can fall apart to soem degree when bad stuff happens. If he lost her later, say early teens which seems to be fairly popular in canon (and had a good r/ship before then), he might be less fundamentally fucked-up but with some neurotic oedipal issues and issues about losing people he loves, worsened by his father's attidue to him (invalidation, trying to force him into the company, not seeing who John really was).
The seriously messed-up Sheppard would have the potential to appear highish-functioning, and to have learned to behave that way as that's what people around him want and what gets him what he wants, but internally to be pretty mistrustful of close relationships, and to tip over into paranoid projection when stressed. I'd see him as being pretty schizoid and avoidant in close relationships. He'd dislike himself and be insecure, fundamentally, while maintaining the false social self which would alter depending on what the person he was with wanted him to be (like sports and Bud with the guys).
Even if you buy the above (and I don't know that I do, although it makes a nicely dark AU), I would still see his physical and military competence as a core redeeming and mitigating feature and as a positive defining factor in his sense of self. Without it I really think he'd fall apart into self-destructiveness or despair. He might have been attracted to the military for some messed-up reasons (outlet for rage, acting out via risk-taking in fighter jets, giving Dad the finger) but the structure of the military probably 'held' and helped him to a degree, despite the need to repress aspects of his character. And again, the need for a false self for the military, and another for Nancy (which didn't work), and another on Atlantis at first when he's thrust into being military commander and literally has to fake it. I think we see him growing once in Atlantis - his 'specialness' to the city would have boosted his self-esteem, and then there are the developing real relationships esp. with his team - the real 'reparenting' experience for him that allows him to become more integrated and whole. I don't think the writers really followed this through at all consistently of course, as they needed him to go on being the slightly mysterious loner/hero who never gets the girl, for the purposes of maintaining the series. They do show his developing closeness to the team especially, although I think his relationship with Elizabeth is more neurotic - a mix of idealisation and treating her as another authority to rebel against. Teyla is the real Mom for him (with interesting oedipal hints of attraction there of course, huh, wonder if his reaction to her pregnancy could be read as sibling rivalry? *g*), and Rodney and Ronon are the brothers he never had (yeah, us slashers all write incest-fic!), given the fucked-up real relationship with Dave. Interestingly, the older male figures are all negative like his real father - Sumner he rebels against then has to kill (oedipus!) and Kolya is perpetually the bad father - controlling and sadistic. Woolsey isn't portrayed as strong enough to be a real father figure although he's definitely benign. I like good fic where Woolsey has that role more for John - a good-father, reparenting figure, like in 'Slide'.
Oh - the flying. Re all the above, I'd see it both as a (mostly functional) escapist defence against the bad stuff, and as a real competence that helps hold him together as a person. He probably sublimates repressed sexuality into the rush of flying, and it would express his need to rebel and get free from controlling authority figures. His dorkiness/nerdiness is also a more functional defence - a small rebellion against his Dad's conservatism which becomes a real part of his core self (humour, quirkiness, competitive games).
And now I'll shut up with the psychobabble!