Somehow your resilience intrigues me...
"Your answer means, when an interferometer is at rest to an observer, i.e. its velocity = 0, length contraction of an arm of the interferometer cannot be used as a mechanism to explain light arrival time independent of earth motion in the direction opposite to incoming light beam. Same with time dilation for light coming in the direction opposite to earth motion hoping to arrive earlier. Interferometer is also at rest to the observer in that scenario."
You want to believe that all of space is filled with an absolute aether through which light propagates and that solves all of the conundrums of science. Somehow you believe that the aether math works without Lorentz invariance and that MEE is also valid as well. The fact that there is no mathematical model that describes both aether and MEE does not seem to dissuade you from believing it and belief is a much more powerful tool of consciousness than reason is by far.
We first of all must make sense out of reality with beliefs that anchor the characteristics of each of our universes and so above all, the universe must make sense. Then, if reason can help better predict action, we can use reason as well as belief and who knows...maybe what we believe and what we reason will eventually be consistent.
First you say the interferometer is at rest...then of course, the answer is easy. There is no length contraction because v = 0. Then in the middle of the sentence, the earth starts to move at 0.47 km/s, but since the interferometer and observer are still at rest, velocity is still zero, v=0, and so the answer is still no changes for the rest frame. Done with the rest frame already...
What you seem to be asking, though, is about another observer in a frame moving at 0.47 km/s and how that moving frame sees the rest frame interferometer. Rest assured that the rest observer measures the same length for each arm with v = 0 even if there is moving observer.
The moving frame measures the arm along the direction of motion as shorter and the moving frame sees the rest clock running slower as well. All the while these measurements of the moving frame do not affect those of the rest frame. This result is a simple consequence of MEE and MEE means Lorentz invariance. Or you can say that the result is the consequence of Lorentz invariance and Lorentz invariance means MEE. There is not one without the other.
Currently there are 12 GPS satellites moving in orbits of 2/d in a gravity that means a 45 microsecond per day gain in gravity time compared to surface gravity time. In fact, each GPS atomic clock is programmed to account for this time gain due to gravity in order to stay synchronized with surface clocks. Furthermore, the relative velocity of each GPS clock results in a time shift of up to a 7 microsecond loss per day at maximal relative velocity and that time loss also has to be carefully accounted for in order for GPS to keep track of objects accurately on the surface.
The GPS system works quite well and depends on a full accounting of both gravity and velocity affects along with its atomic clocks. It is not at all clear what kind of math would replace the very well known gravity and velocity affects that science has measured and remeasured so well on earth and in earth orbits.