Cool article. I have been looking into this myself. Have you come across the Huygens-Fresnel Principle? From what I’ve gathered from others, it produces indistinguishable results from the Path-Integral formulation. The big difference is that Huygens-Fresnel describes light as a spherical wave in 3 real dimensions (like a helix). Interestingly, when we project a helix onto a 2D plane from the side, it looks identical to what we have now, a sine wave. Maybe the complex part might just be capturing the lag of the particle as it rotates around its center moment along a z-axis? Check it out!