I think the key to understanding more , about the precision of your question, is " Have you considered that , for multiple vectors, we might have both dynamical and non-dynamical spin operators for any given model". Once you select a frame of reference for the fields, only one of any two spin operators will appear dynamical. Based on your question, this is how I imagine the method of problem and it's attack. I am open for other expert opinion just the same. Even if there are , in definition, two dynamical vectors, can't the model be rewritten , with reference, as I am suggesting, to the useful simplification to determine the information you require?

A simple way to test this is to design a sufficient example of modelling the spin, is to question whether the model properly includes an integral, and whether that integral can show or prove to be complete if the spinor or spinors are elastic. Maybe thinking of it in this cognitive way allows one to understand the relativistic property within the spinor prior to understanding it between two spinors (in a complex way)

The other problem in applied physics is that the path function for the electromagnetic dipole is only somewhat dependent on the discrete paths for relativistic functions. The dependency is most closely related to it's ability to emerge along it's own axis (path). The charge differential is an inertial mechanic that has this "elastic feature" which is why I made this previous comment. That means some aspects are field co-related, and some are not. It is too early in my own work to state publicly how I would explain the rest of the equations for completeness, but I don't think the math in your example can model the whole set of physical parameters. This is best demonstrated in attempts to perform the most basic analysis of the fields for the Hydrogen atom