Ken,
I agree a Lagrangian approach, indeed I've argued that the centre of a large mass such as a SMBH should not be a singlarity but a point of equilibrium. This is precisely a Lagrangian point, and gives a toroid form of gravitational potential, a form common to all em fields, tokamaks (fusion) and which I deal with every day as an astronomer, as AGN's etc.
So of course maths (see my end note terms) but far more warily. Information theory shows your idea can be taken further (See McEachern essay) because the information possible in a mathematical abstraction is tiny compared to that contained in what it is trying to model (nature). I'm thus far more rigorous in applying the order; Correct concept first, Maths second. This requires the structures of logic, and a fully consistent ontological basis, which few of our theories posses. Expecting maths to accurately match reality is then foolish.
My main point is that, if we drop the series of related and unproven assumptions identified, the gap between SR and QM disappears. SR is derived direct from QM, and consistent with GR. CSL, curved space-time etc are all natural and inevitable consequences and effects of a single and well evidenced (but poorly understood) series of real mechanistic quantum interactions. The picture is Einstein's Local Reality, with causality conserved and paradoxes resolved.
The strict construction of truth propositional logic (hierarchical frames), and Dynamic Logic (interleaved but non interfering modes) are followed.
The evidence is overwhelming, but the big issues with it are that it's;
1. Entirely unfamiliar.
2. So self apparent we can't possibly not already know it.
3. Hiding so close in front of our eyes it forms a layer on our lenses.
4. Far to 'big' and fundamentally important to be recognised or acceptable.
5. Does not require complex mathematics to initially find, just visualisation of the evolution of kinetic effect (a new way of thinking).
6. Although it agrees with the SR postulates, it finds a fault in one of the the assumptions used for SR so must of course be wrong.
Could you see any of that? I'm considering reverting to the incremental approach (paper on resolving the Kantor interferometer issues accepted and due soon). Any other ideas?
best wishes
Peter