It isn't true that the bottom up approach "has already been challenged over the last century or so". The approach continues working fine.
"each emitted wave function". Wavefunctions aren't waves they cannot be emitted.
dp/dt=qE is valid for the average momentum not for the fluctuating p.
SR doesn't apply to extended bodies as the wheel. The no-interaction theorem states that LI is not valid for particles with permanent interactions.
Photons don't change mass of wheels. Mass is constant and given by E_0/c^2. Photons change E not E_0.