Even when the Earth is further away, the moon will be seen to appear later, sure, but it will also disappear later - so the measured times between disappearance and appearance should be the same
When the Earth is far away, the moon will be seen to appear late, but it will also seen to disappear late - so the measured time between disappearance and appearance is not affected by the distance, as disappearance and appearance are equally affected by the distance, when the distance is the same distance for the disappearance and the appearance.
When distances are not the same distance for the disappearance and the appearance, then the measured time between disappearance and appearance is affected by the difference of distances.
When you move away from Jupiter at the speed of light, the appearance Io seems to never happen after the disappearance of Io. As we only observe a slight increase of time between disappearance and appearance, we know that the speed of light is many times the speed at which the earth moves away from Jupiter.