Hi Burt,
I met a guy named David Cooper on another forum, and he succeeded to convince me that the length contraction of relativity was right. He did a very nice simulation of MM experiment using LET (Lorentz Aether Theory) as a basis for propagation of light.
My problem with relativity was that I did not understand the beaming phenomenon. In David's simulation, a laser is sending a photon at the future position of the upper mirror even if it is pointing at its actual position, and I couldn't understand why, so he simply told me to observe the way the photon was traveling in the laser while it was moving to the right, and I finally understood that only the photons already moving in the right direction in the laser could be reflected properly at its ends, in such a way that when they finally get out of it, they are actually traveling towards the interferometer's mirror. His simulation shows that only a contraction of the interferometer would permit the two photons to travel the same distance in the two arms, so this way, length contraction was easy to accept, but I still had a doubt on time dilation even if a photon would visibly travel more distance through aether between two moving atoms.
I said it would work if moving atoms were sending photons one at a time and if they would wait for the other atom to send it back, because then, the photons' frequency would be slower than with atoms at rest, but why would atoms do that I said, and he referred me to his Twin's paradox simulation this time. The solution of the paradox resides in the speed a ship has to get to catch up with another ship that has been traveling away from it for a while, and that is still traveling away at the moment the other ship tries to catch up with it. That ship will have to move so fast that, when they will meet, his clock will have slowed twice as much the clock from the other ship has. This way, wether we take the earth or the traveling twin as a reference frame, the result is the same: the twin that has to turn around if the earth is considered at rest stays younger. Have a look at his simulation for a better explanation. That's the first time I saw this paradox solved in a convincing way, so I began to believe Einstein was right about time dilation and length contraction, and I immediately tried to apply them to my small steps. (Feel free to send the rest of my post to Personal Theories if you feel that my conversion is not complete enough :0)
Atoms cannot emit photons without being accelerated or without absorbing an incoming one, so we can imagine that two atoms that are part of the same molecule could exchange indefinitely a photon that one of them would have emitted while it was accelerated, providing they could do so without loosing energy. As I said to David, I certainly cannot object to that mechanism since my small steps depend on it, but while looking at the distance my photon would travel back and forth, I realized that it would be different whether the atoms would be approaching or getting away from one another during their steps, and it has to be the same otherwise the steps wouldn't be the same.
So I juggled with the idea for a while until I realized that my steps necessarily had to suffer length contraction, and that any contraction due to motion had to happen at the beginning of any acceleration. If we accelerate a first atom which is part of a two atoms' molecule, it necessarily moves before the information from that acceleration has the time to reach the second atom, so the distance between them contracts, and if we are still accelerating that first atom while the information from the motion of the second atom is back, that information will simply pull the first atom forward a bit while it accelerates, so the distance between the two atoms will contract a bit more than previously, and it will go on contracting more and more until the acceleration ceases. At that moment, the information about the speed of the two atoms will be contained between them in the form of doppler effect: the rear atom will perceive redshift from the front one, which will pull it forward, and the front one will perceive blueshift from the rear one, which will push it forward. Contrary to my original small steps, during the motion of the molecule, the two time shifted motions of the atoms would thus happen at the same time, but those motions would still be due to the accumulated doppler effect between the two atoms. Here is the diagram and the explanations that I gave to David:

We have two atoms A and B that are part of the same molecule. The time interval represents the time the information takes between the two atoms at t0. I did not account for the time dilation of particle A since it moves before particle B, but I think we should. We accelerate A for a while and observe what happens to the system from t0 to t7. The blue arrows represent the blueshifted information that travels from A to B, and the red arrows represent the redshifted information that travels from B to A. The acceleration of A begins at t0 and ends at t4, so because of the time gap, the acceleration of B begins at t1 and ends at t5. After t5, the two atoms travel at the same speed, but we can easily see that the distance between them has contracted, and we can follow its progression during the acceleration. At that moment, the information on the future speed of each atom with regard to aether is situated between them in the form of doppler effect. The main idea is that, without doppler effect, there would be no motion between bonded particles, so there would be no motion either at our scale. I insist on the fact that we have to exert a force to introduce that doppler effect between them, and that this force represents mass. So with the same principle, we explain mass, motion and contraction. Of course motion is a bit more complicated this way, but we can discard the complicated Higgs, and we can study more closely what happens with motion at the micro scale, which could help us to link Relativity theory to Quantum theory.
Now what about time dilation? Can my small steps benefit from it? As David's simulation shows, a photon would take more time between my two atoms since they are moving, so the frequency at which this photon makes its roundtrip between them should be slowed, and that difference should show if we observe them while we are at rest, but what about the acceleration the first atom suffers before the other has moved? Would it add to the doppler effect? Soon to be released on your screens! :0)