I think a conventional double jaw surgery should be enough for you. Mid faces are tough to evaluate aesthetically even for trained surgeons. A Le Fort I advancement will take away the flat look, but it won't give you "plates of armour" right under your eyes. It will sort of "tent things up" and give your face more depth and make the orbital weakness less obvious. On the other hand, there is a chance of coming out looking a bit "chimpy". I would also consider a zygomatic osteotomy. Hard to give this advice given that I've only ever seen those "sandwich" ZOs done by MM, and the improvement looked marginal... but it should theoretically give you more facial width and take away the "long flat" look.
I know the Obwegesser demon->angel girl gives everyone the vapours, but I've only ever seen modified Le Fort III done on ridiculously recessed class IIIs with bulging eyes. OK, she did not have bulging eyes, but she was a pretty severe class III.