Zig-zag model illuminates helicity vs. chirality?

[Spinnor]

Can we use the Zig-Zag model of the electron to get an intuitive understanding of the difference between helicity and chirality?

Suppose we have a long and narrow cylinder where the spin 1/2 massless zig and zag particles bounce between the top and bottom of the inside of the cylinder at the speed of light. Label one end of the cylinder as the top. The zig and zag particles change into each other when they bounce off the top or bottom of the cylinder. There are two possibilities, the top end of the cylinder changes zig to zag or zag to zig, this gives spin up and down? (The zig and zag particles have opposite chirality and spin.)

Edit: The zig and zag particles have opposite chirality and the same spin.

With the cylinder at rest and pointing in some direction the zig and zag particles exist for equal times, have equal magnitudes of momentum, and left and right chirality exist for equal times. Now consider what a person sees if they move rapidly past the cylinder with the top of the cylinder "leading the way". Now zig and zag particles don't exist for equal times, they don't have equal magnitudes of momentum, and left and right chirality don't exist for equal times, the zig-zag particle "becomes" chiral?

The faster we move past the cylinder with a given orientation It will "flatten" and "appear" rotated into alignment with our velocity? Helicity and chirality become the same?

Thanks!