People often worry about tire wear when in reality it doesn’t really matter. What matters is the stopwatch, so I wouldn’t worry too much about it.
If you think the coning is excessive (more than your competitors’ tires) but you can’t get the kart to stop oversteering when you add camber, that sounds like a driving issue to me. It sounds like the kart might be understeering with negative camber which means it’s really stable, but you’re burning up the fronts. Your driver might be too harsh on the wheel and when you put front grip into the kart, he isn’t adapting his driving to the increase response in the front end. Something I would try would be to incrementally add small amounts of camber to the front over a practice day and see if he can adapt over the course of the day. You might find if he slows his hands down, he can run with that extra front grip and be faster.