Ooh I like this!
I'd start by making braces as a whole a lot less common. Reserved particularly for those who have a great need for it, but aren't excited about it at all, and those who may not need them as badly, but seem to want them in an almost strange way.
I'd make it uncommon just enough so that when someone DOES have them, people notice. People talk, and that person becomes "that one with braces". You're instantly the metal mouth of the crowd.
In terms of the metal itself, full bands are used in conjunction with garishly bright colors chosen by the patient. They'll have a say in what colors they get to sport, but all the options will be bright and eye catching. In addition to full bands, every patient gets a bulky tongue crib that's continually adjusted to maintain a patient's lisp, with the idea that tongue thrust is such a serious concern for how it can distort the bite once braces are installed, it's better to prevent it outright with a tongue crib cemented to the molars for the duration of treatment.
Upon the very first appointment, before bands are cemented, the patients vision is tested. Even if their eyes are fine, prescription glasses are assigned and made to be worn. Don't worry, their eyes will adjust.
What's more, everyone who has to go through the ordeal of "becoming a braceface" knows that headgear is inevitable. After all, it supposedly moves teeth faster, and even if you dont have an overbite that's THAT bad, they'll just use the lowest traction possible and use the Anchorage to stabilize the movement of teeth. Once it's your time to get headgear, you know it's going to either be worn 12-18 hours, or the orthodontist might just up and decide to wire it in. It's a coinflip's chance. Everyone knows they'll end up getting headgear, but no one ever knows when. It could be at your first appointment, it could be after 3 years of braces, but you'll never know until that appointment where without warning they're placing the facebow into your mouth.
Being a braceface would be an ever present atmosphere that follows you, marks you, and you're stuck like that for as long as it takes.