Chapters 17 (there's a section about collusion in trivia and puzzle games) and 18 (high-score security) seem especially relevant to your interests. In fact, page 186 talks specifically about "Replayable Game Logs" as a technique to detect cheating, just like you said. However, it says:
This was somewhat true at the time of writing, but is no longer the case now (since we now have webStorage).
Chapter 20 talks about tournaments, and how some players work to disrupt and cheat them - this seems especially relevant since you're planning a contest.
Chapter 31 talks about gambling: "Skill games, contests, promotions" which is also, again, insanely relevant to your game, especially since you want to offer prizes.