Hello Geoffrey,
Good metaphor, thank you. Immediately we bump heads, tho, with C more fundamental than R. Given that the goal in our two essays is to have a satisfactory model of agency in the physical world at the level of the elementary particle spectrum, I'm of the view that R is more fundamental than C. This is the position taken by the geometric algebra community of the 'Hestenes school', as so simply and lucidly presented in his 1966 book, Spacetime Algebra, which resurrected Grassman and Clifford's original geometric intrepretation and introduced it to physics.
In the geometric view one can take the vacuum wavefunction to be comprised of the eight fundamental geometric objects of the 3D Pauli algebra - one scalar, three vectors (3D space), three bivectors, and one trivector. Endowing the geometric objects with topologically appropriate fields, this becomes an agent in the physical world.
Interaction of these agents/wavefunctions can be modeled by the nonlinear geometric product, which generates a 4D Dirac algebra of flat Minkowski. Time, the dynamics, emerges from the interactions, encoded in the 4D pseudoscalars. There is no need for complex numbers, for complex algebras, for this particular legacy of Euler.
re spinors, they are likewise understood as being comprised of a scalar plus bivector, can be visualized. Reinvention of Clifford algebra by Pauli and Dirac in the matrix representation has left the community stuck with something that is too abstract. Basis vectors of geometric algebra are equivalent of matrix representation....
I admire your knowledge of group theory, a knowledge that i sorely lack, hope that the above outline of the geometric wavefunction is helpful to you in applying that knowledge to the physics.