I would say just include a code inside the box that you can type in to validate your review as an actual purchaser. Then Amazon could heavily weight these reviews, at least for products known to be prone to scam reviews.
They already have a system for this: "Amazon Verified Purchase" will appear below the title of a review from someone who bought the book. Of course, they had to have purchased it from Amazon. They could default to only showing verified reviews by default or weighting verified reviews higher than unverified ones. It's too easy to create accounts and reviews to keep letting this just slide.