I think by coming up with "cheating-proof" assignments you'd be ignoring the real issue, which is that students think it's ok to cheat.
Why would that be the case? I mean, if the assignment naturally disfavors cheating (by making it more trouble than doing the assignment honestly), doesn't that send a pretty powerful message to the students? "You might have gotten away with cheating in other classes, but in this one, you'll really have to work." It seems like it would be the same message as a strict anti-cheating policy, but without the acrimony.
Why would that be the case? I mean, if the assignment naturally disfavors cheating (by making it more trouble than doing the assignment honestly), doesn't that send a pretty powerful message to the students? "You might have gotten away with cheating in other classes, but in this one, you'll really have to work." It seems like it would be the same message as a strict anti-cheating policy, but without the acrimony.