Do you know why it uses oil? Is it the piston rings, or something else? Have you checked your PCV system, for example?
For an oil burner that doesn't otherwise need a super-tough oil, I'd try Mobil 1 Advanced Fuel Economy 0w-30, Mobil 1 ESP Formula 5w30, Castrol Edge 5w30, or Pennzoil Ultra 5w30 before I'd try GC. GC has a heavier dose of additives for use in high-performance applications with extended drain intervals; I don't think that'll help you, and it might even be counterproductive since those additives can leave deposits over time. I suspect that all you really need is an oil made from good base stocks and a "clean" additive package, so that it retains its viscosity in your piston rings and burns as cleanly as possible when it does burn. Just my thoughts.