Why not rotate the 1/2, 1/3, and 1/4 measures by 90°, 60°, and 45° respectively? Now they are symmetric and still stack nicely.

This is actually the sandwich problem, which states there is exactly one slice that will split a sandwich of 3 elements into exactly 2 halves regardless of the shape or position of those elements. We don’t need the full proof, but the problem is continuous, so any desired ratio is possible, therefore you will always be able to slice an apple into exactly 1/3 and 2/3rds “good bits”, so a single slice will always be able to do the job.