The Masamoto HC should fit, but I have no personal experience. Anyway, it's far beyond your budget. I know the K-Sabatier to come very near to that description, though. But their carbon steel is much softer.
By the way, with a Misono or Hiromoto 270 you don't have to worry about stiction, even if the spine is about 2.5mm. The right face convexity is very obvious.