The original design is nice, but it doesn't work very well due to the pegs going through the maze being shaped from a sphere. I redesigned the pegs to better fit the shape of the maze. With the new design you don't get stuck as easily and you don't have to use force or increase the size etc of the outer part to make it work.
I printed without any support, so should be fine for you as well.
Maze_outer_part.stl | 166.5KB |