No problem. The time dilation of that longitudinal light clock consists of two time delays. We may call the time delays Doppler shifts too. A Doppler shift is a quite large effect, while time dilation is quite small effect, at low speeds, and so is length contraction. How small effect is then such time dilation that is caused by length contraction. It's a very very very small effect at low speeds.You're right then. Do you see a problem with that?