Lev
The issue is not the choice of representational device, per se, but how it is organised in order to properly correspond with physical existence as it occurs, and not how we think it does so.
There is nothing inherently wrong with considering 'space', because physical existence is a spatial phenomenon. The main problem has been the representation of time, which relates to the rate of change, ie a feature of the difference between successive realities, not of any given reality. In other words, unless that is understood then space can be misconceived (obviously in terms of detail it can be mis-represented by flawed representation). There is no duration in any given existent reality. So when distance (space) is expressed in terms of duration, it is conceptual, not physical. The concept being that it can be measured as the duration which would have been incurred had any given entity been able to travel along it, either way. But this is not possible, because there is no duration available during which that can actually happen. So it must be understood that there is no duration, as such. That is, the result is just an alternative expression to, and the equivalent of, a specific spatial measure. Misunderstanding this leads to the flawed application of the equation x = vt.
Although you do not explain it, the concept of measurement is comparison to identify difference, and for such differences to be comparable this needs a constancy of reference. Again, assuming the correct presuppositions and adherence to due process, this is not a problem. Indeed, it is the only way to proceed in a closed system. The point being that we only have knowledge of. There is no direct access to reality. We are compiling knowledge by comparing knowledge, with the objective of being able to declare it the equivalent of physical existence. Because physical existence is all that which is potentially knowable to us. The concept of information is a fallacy.
"The known physical forces cannot account for the structural regularity of these formative processes as reflected in the observed classes of similarly structured objects, e.g. various classes of stars, galaxies, stones, trees".
The whole point is not about representation, per se, but about correspondence with what is being investigated. Any representational device, and the way it is ordered can be valid so long as it accords with physical existence as it occurs. And that is where the problem lies with physics, the underlying presumptions are incorrect, not the application of maths, etc. There are no 'objects' and there is no form of indefiniteness in physical existence. This is a flawed representation of reality based on a higher conceptualisation than what occurs. That is, we are deeming existence on the basis of superficial physical attributes, which are then considered to change. A contradiction in itself. What exists at any given time is a physically existent state of whatever comprises it. At another given time there is a different physically existent state. There is a reason(s) for the difference. Different is different. It is not the 'same but with changes'.
So unless your alternative representation system recognises that, then it will be no more valid than the systems you strive to replace.
Paul