Your only quantitative response above dealt only with energy, as far as the transverse motion goes, not with momentum. Your only response to the question of the transverse momentum of the electron has been a vague analogy to radio antennae or television aerials. You have not demonstrated quantitatively that both momentum and energy are conserved. You brought up the simple model with three electrons. You need to actually show that the additional two electrons can provide the necessary restoring forces for the electron to oscillate, and that you can account for the energy lost by the photon while also balancing the momentum. A handwaving argument won't suffice.