Thanks! The grid based movement is unfortunately a limitation of Pulp. There are ways to fake smooth movement or rather create the illusion of it, but the movement will still be tied to the grid.
I think it would look better, but I'm not sure if it would feel better, at least not for player movement. The movement would be less responsive due to "input lag". The player technically moved but you have to wait for the animation to finish before you can do your next action. It would probably work for a game without combat or at most range combat. Not so much for melee combat.
If things go well I will look into porting the game to PC or Gameboy with proper smooth movement. :)