The Lienard Wiechert potential is the convincing reason. The LW potential depends only on the motion of the charge at the retarded time. So the field at the near side updates with ~1 ns delay and the field at the far side updates with ~1 year delay. The field does not change outside of the times as indicated above.
If you are not willing to accept standard solutions like the LW potential, then there is little that can or should be done to convince you.