I imagine that would be quite difficult to do.
Difficult, yes, but possible if there's a will to do it. They'd have to start by offering a standard curriculum city-wide in the lower grades and providing schools or programs for gifted kids in each neighborhood, and they'd have to provide seats for every kid who scores in, say, the top two or three percent for that neighborhood. Just by guaranteeing seats, you ease some of the competition strain. You might also ease other strains, too.
Then they'd have to be very secretive about the contents of the exams. CTY takes this approach with its SCAT exam, and so do the people who make the Miller Analogies test. You can get enough information about each exam to understand the
format of the test, but nothing else, really. They don't really release previous exams, and this cuts down A LOT on how much you can prep for these tests. I believe that it's generally agreed that you can't really prepare for an IQ test either (apart from learning tricks to remember number sequences?).
But again, I think what they really need to do is provide a seat for any child who qualifies. Not to mention that they also need to pay attention to the ones who were close, but didn't qualify.