At some level this is just the application of wave mechanics to reality. "A vibration on a guitar string is just the sum of the vibrations of its harmonics." Yo

At some level this is just the application of wave mechanics to reality. "A vibration on a guitar string is just the sum of the vibrations of its harmonics." You are decomposing a system into a mathematically favorable basis, performing a calculation in that basis, and recovering the original basis (by linearity). You can do this in a hamiltonian way (find the eigenvectors of the hamiltonian, decompose your system into those, step them forward [easy] and add them back together) or in a lagrangian way (treat each point in the system as the source of a sort of spherical wavefront). Feynman is doing the latter - he's just asking "what if we treated other fields the same way we know we can treat the EM field via Huygens-Fresnel?" Calculate the progression of wavefronts through the field, using euler-lagrange to find the parts of the wavefront that don't fade away into random noise. So, in the framing of your question, I think it's mostly B and C, with maybe a bit of D (it's not clear if we have any kind of tool besides aesthetic preference to distinguish between extrinsically equivalent models). However, your framing might be a bit uncharitable.