Thanks for the comments Uncle AI. I can respond to two of your points and, at least partially, answer your question.
Firstly, I agree that the prediction of "magic islands of stability" is not an easy task - and in fact most of the even proton numbers from 106 to 126 have been predicted at one time or another to be the location of an island of superheavies. Still, for many years, Seaborg and colleagues have been adamant: "One fact should be emphasized from the outset: while the various theoretical predictions about the superheavy nuclei differ as to the expected half-lives and regions of stability, all theoretical predictions are in agreement: superheavy nuclei can exist. Thus, the search for superheavy nuclei remains as a unique, rigorous test of the predictive power of modern theories of the structure of nuclei." (Seaborg & Loveland, Contemporary Physics 28, 33, 1987). If "existence" means isotopes with lifetimes of a few milliseconds, then Seaborg was correct, but the actual predictions have been much more optimistic than that. For example, Moller and Nix predicted a magic island at Z=114 with a half-life of 10^14 years (Journal of Physics G20, 1681, 1994), but the empirical reality is in the millisecond range and nothing above Z=115 has been discovered or constructed. Already in 1989, in a monograph entitled Superheavy Elements (Hilger, London), K. Kumar declared this to be a "crisis of nuclear theory" because the theory that is believed to be correct and is used to calculate binding energies seems not to predict the actual situation. On the strength of theoretical "certainties," funding for such research has been abundant for decades. To be sure, many interesting things have been discovered, but the theory of the nuclear force that has motivated superheavy research appears to be incorrect, so that, after more than 40 years, is it not fair to ask what conclusion might be drawn from what Seaborg and Loveland called a "rigorous test of the predictive power of modern theories of the structure of nuclei"?
The failure of superheavy research is arguably a good example of your second comment. The independent-particle model - which remains the central paradigm of nuclear structure theory - can be used for interpolation, but extrapolating beyond the known range of stable/semistable isotopes simply doesn't work.
With regard to your question, Wigner's geometrization of the Schrodinger equation applies to all known isotopes - not just small nuclei. In other words, insofar as the IPM description of nucleon states is accurate, Wigner's geometry (the antiferromagnetic fcc lattice with isospin layering) is also accurate. (Wigner himself took it up to Molybdenum, but others have generalized the technique and shown that it precisely follows the harmonic oscillator indefinitely to the largest nuclei and beyond.) In that regard, the theorists are in agreement and experiment is supportive. The remaining question is then how should we interpret the geometry of this known pattern of nucleon build-up. With so many correspondences between the lattice and known structural properties of nuclei (radii, alpha structures, shells and subshells, etc.), it seems perverse to suggest that it is all just a huge coincidence, but if the correspondence is truly with coordinate space, then nuclear structure theory based on the Schrodinger equation needs to be reconceptualized as "standing waves" without the "orbiting" of nucleons that are so densely packed that there is virtually no empty space between nearest neighbors.
