Requiring participants to have certain number of merits was the best thing you could do and you did it. There should be a requirement, a minimum post count, a minimum activity or minimum merits. I think minimum merits is the best option and I personally cannot find a better solution.

As you said, there are some competitions in "games and round" board. Some owners don't bother themselves to make a rule. Some of them say that using multiple accounts are not allowed, but actually they do nothing to fight multiple accounts. Most of those competitions are due to promotion and advertising purposes and owners don't have any issue with multiple accounts. Because multiple accounts help their thread be more active and this is exactly what they want. But your giveaway is different from them. You are paying the reward with your own money, want to have a fair competition and have to make a rule to avoid cheaters.