Erik,
A truly interesting essay on the impact and assessment of a Unified theory in Physics.
Tetryonics - the charged geometry of EM mass-ENERGY-Matter may well fit the bill as it is based on the priori principle that equilateral energy geometries are the foundation of all physical forces, fields, particles and their interactions.
Whilst you argue that theoretical physics is Mathematics, I would argue that Physics is GEOMETRY which in turn constrains the Maths that describes it.
An important point to reflect on here is that whilst Tetryonic's equilateral geometry changes our view of Energy in all its forms it does NOT change the Math used to describe the physics [save for where it reveals errors in the current formulation or physical perceptions of the Math], in complete agreement with James Jeans' statement in your essay.
You will note that even Einstein advised against the "prejudices of known facts" as highlighted at the beginning of my essay and that Tetryonics goes a long way to prove cautionary statements like that to be sage advise.
Through its equilateral geometry many mystifying aspects of physics are swept aside and revealed to be facets of a foundational equilateral geometry.
Perhaps the best examples of this is the early revelation in Tetryonics that SQUARE numbered energies in QM are in fact TRIANGULAR geometries, and that quantised angular momentum is not a rotational vector but a measure of equilateral geometry per unit of Time. [see attached].
To date I have applied it to QM, QED, Chemistry and Cosmology [as well as SR & GR] and I hope you'll examine Tetryonics [both the essay and my detailed work on the net] and see how it meets your criteria for a unified field theory of Physics.Attachment #1: 2_Figure_80.22__Geometric_Physical_Maths_800x600.jpgAttachment #2: 2_Figure_01.07__Quantised_Angular_Momentum_800x600.jpg