Ten years of free protection, then costing $10 × 1.5 ⁿ ⁻ ¹ for each subsequent year. Year 10 costs $0, year 20 about $380, year 30 about $22,000, year 40 about $1,300,000, year 50 almost $75,000,000—and few fifty-year-old things will be worth $75,000,000 per year and growing to retain copyright to. And I doubt any individual work would be worth the $4.25 billion of year 60 (10 × 1.5⁴⁹, incidentally just 1% short of 2³²), so that’s a rough absolute cap of 60 years.
You could scale the $10 base figure to inflation, or you could just schedule a review every decade or so, or you could even ignore inflation altogether, which would slowly extend average copyright terms (e.g. year N today would cost similar, indexed, to year N+1 20 years ago).
Concerning your registry, I don’t think you want to require a registry for the first ten years, but only for any extensions—and make it that if anyone can prove beyond reasonable doubt that you actually published the thing earlier than the date you claim when you register it, then your work is thrown into the public domain as punishment.