honestly, I don't really see the contradiction with GTD in what you describe . Picking a project (THE project) you want to focus on more than any other during the week (3-10 days as you say it) can perfectly be part of the weekly review. It's really up to you whether you pick a project that makes you really move forward or just any project that seems interetsing.
By the way:
You say ""Set up your 20,000ft review, and then reanalyze your priorities every time you complete a task." It's not working for me."
But... that's in fact exactly what you did... You mention "I replied to as few emails that don't deal with this project as possible"... that means you reanalyzed your priorities with every mail you read asking yourself if it was important enough to deal with or not.
So, I would say that your approach is completely in line with GTD...