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It seems that Testmasters, Powerscore and Blueprint use the same methods with different nomenclature. Is there another methodology less reliant on scenarios and initial deductions? Preferably in book form?

They'll all boil down to maximizing initial deductions and making scenarios whenever possible—at least in my experience. I found that the Powerscore LG Bible provided a strong base, with the Manhattan LSAT Strategy Guide closing the deal. With these two books and a lot of drilling, the games become second nature.

I find mastering individual games helps you see where similar deductions can be found on all games. Initial deductions and local diagrams are key.

7Sage has some good, free logic games explanations. You can use them to be sure you've mastered individual games.