The situation is as follows: Physicists are doing A. Neo-Lorentzians do B which contains A, but hides it and then claim they do not need A, as they did B. The Universe simply has length contraction and time dilation. If you call it fundamental or "effective" does a priori not matter. They are there, you have to compute them. Even worse, when you switch to the reference frame of an accelerated observer, you inevitably get curvature, since your curved line getting straight, means straight lines will become curved. You will also see that the rate at which time gets dilated depends on the distance from you and (in more complex situations) the rate of length contraction is dime dependent. I am btw. referring to Rindler coordinates and proper coordinates. Having established this, you will have to deal with that. You will now go to your mathematician of choice and ask him "Hey, I have here some phenomena which contract and curve space and time. How do I mathematically handle that?". They will answer: "Well normally lengthes and angles are described by metric tensors on manifolds". So you take, what they give you and build a physical theory with that math. What you will end up with is special and flat general relativity....
