I think stealing picks from a contestant who's just behind you is a much, much bigger problem, potentially.
Anyone with a realistic chance to win should have an option to PM picks to admins... for at least the final week.. maybe 2 weeks.
If you just pick a realistic line, or even 2 cents better than current line at a given book, there's maybe 5% chance it will end up moving you up the ladder, even over 100-120 picks.