Finding students with integrity is hard now, because the culture is already full of poo.

But one starting point is to communicate that you expect and require integrity, explain what that means, and then expect it. Trying to make metrics or tests or whatever to detect, rate, rank, etc. it just turns it into a game, like the same load of poo.

Though here is one thing you can do. Explain that you expect integrity, and then watch the students raise their hands and ask how they will be tested on this. You say it's expected. Back and forth a few times, until eventually some of them start crying, and then their heads explode, because they can't figure out how to game that. Those students sadly were too far gone.

Then, after that first semester of integrity culture, some of the students who didn't explode will cheat, and they will be expelled with the fury of an angry god, and everyone on campus will know why. News stories will be written, word will spread, college guides will be updated. The next batch of applicants after that will have fewer cheaters than before, and will have disproportionately attracted students who aspire to integrity and who wouldn't have known to apply to this school before the news.

A school with an honor code that students and faculty take seriously wasn't that newsworthy decades ago, but it's news now.