Consider the distribution of the entered projects. Due to the selection process (think evolution-style selection rather than "human judging" selection), all the projects, whether purely-student-driven, student-driven with just a dash of parental help, half-and-half, and the student basically along for the ride as the parent runs a project, are in one big pile. Is there going to be a bright, sharp dividing line? Especially in light of the fact that quality is only going to be loosely correlated with external help?
Perhaps this is an unpopular call but my personal opinion is that the whole idea of a "national scale" science project contest is irredeemably flawed and the correct answer is simply to discard it. It is a common flaw in thinking, often expressed by many commenters zealous to "correct" other people, that if you can't draw a bright sharp unarguable line between the various elements of a group of some sort that you can't claim the group "exists". This is nonsense; almost every practical grouping scheme will always have borderline cases or exceptions. But there does need to be some sort of actual grouping, or some sort of relatively objective way to sort and categorize the elements, that is accessible to the sorter. In this case, while from the objective divine perspective maybe we could create an objective standard for who got "too much help" to be qualified, there is no conceivable world in which the contest judges could ever get sufficiently accurate information to be presented with anything other than a very smooth gradation that they simply will have no handle to make a correct decision with. So the incentives will always be to get as much help as possible and then have human-intelligent agents doing their best to fool the human-intelligent judges, and that's just a hopeless situation.
Of course, the contest will not be shut down. But what can happen and what may well happen is that it will get more and more embroiled in controversy each year as the game-theoretic local optimum approach for the contestants each year becomes more and more to accuse their competition of being "too helped" and thus take out the competition until it is simply a farce. This is the worst game-theory case for cooperation; very limited repetition of plays by any given participant, most likely one, so no reason to care about the integrity of the contest for next year when they won't even be participating most likely.