In AWT Lorentz symmetry(LS) is direct consequence of observational perspective. When we are observing low dimensional space (like 2D+1T water surface) from strictly 2D+1T perspective, LS is indeed maintained. When we are observing the same situation from higher dimensional perspective, LS can be violated and nothing very special is about it. AWT stance is, every space-time is completely homogeneous from its own perspective by definition and its LS cannot be violated. At the moment, when we are discussing some homogeneities in it, we are applying higher dimensional perspective, which enables LS to become violated. "An Outside View" is always of higher dimensionality, then insider's view, so its LS can be violated by definition. If it wouldn't, we couldn't distinguish it from inside view, after all.
In AWT concept of minimal length doesn't exist from global perspective, because even the tiniest density fluctuations can be formed by some more smaller ones without apparent constrains. But there exist limit in observability of smallest density fluctuations from perspective of larger density fluctuations (like humans) or instrumentation, which was used for their detection. Aether fluctuation at particular dimensional scale cannot interact with fluctuations at all remaining dimensional scales directly in accordance to principle "Simillia simillibus observatur". If we would use more sensitive/large apparatus, the limit of fluctuations on both sides of dimensional scale will increase accordingly and we would observe our Universe larger and quantum fluctuations smaller - but some general limit still persists here.
The philosophical question is, if such dimensional scale is real for people, because it's always interpreted by apparatus. Science answered such question positively already from the time of Galilei and van Leeuwenhoek. The main gnoseologic problem is, outside perspective remains undetectable from insiders, so we are always talking about somehow abstract phenomena, which can be proven by higher dimensional emergent approach only, i.e. by coincidence of two or more indirect evidences - but not by direct observation. Whole evidence of emergent Aether concept is about it, after all.
It should be pointed out, the existence of space-time at sub-Planck scale (i.e. existence of "subminimal length") lies outside of observational perspective scope of insiders too, so we are relating existence of one unprovable phenomena (Lorentz symmetry violation) by existence of another one (sub-Planck length).
Proclamativelly rigorous people, who are working with insintric perspective preferably can say easily, both ideas are BS - whereas other people, who knows, that more is different and really is different and how emergent phenomena are working, can expect, combination of two or more undetectable phenomena (assumption) could still lead to new observable (i.e. testable) predictions, thus fulfilling utilitarian perspective of further evolution. After all, renormalization procedure is quite similar approach based on emergence, because its extrapolating singular function by pair of their derivations from both sides of divergence. In this way, modern physicists just replaced wide-scale philosophical extrapolations by these less-visible formalized ones.